3.3: Payroll

Introduction

You work hard at your job, and you want to be compensated properly for all the hours you put in. Assume you work full time with an hourly rate of pay of [latex]\$10[/latex]. Last week you worked eight hours on Sunday and eight hours on Monday, which was a statutory holiday. Then you took Tuesday off, worked eight hours on each of Wednesday and Thursday, took Friday off, and worked [latex]10[/latex] hours on Saturday. That’s a total of [latex]42[/latex] hours of work for the week. What is your gross pay? Give or take a small amount depending on provincial employment standards, it should be about [latex]\$570[/latex]. But if you don’t understand how to calculate gross earnings, you could be underpaid without ever realizing it.

Here are some notes about the content in this chapter: About [latex]10\%[/latex] of Canadian workers fall under federal employment standards, which are not discussed here. This textbook generalizes the most common provincial employment standards; however, to calculate your earnings accurately requires you to apply your own provincial employment standards legislation. Part-time employment laws are extremely complex, so this textbook assumes in all examples that the employee is full time.

This section addresses the calculation of gross earnings, which is the amount of money earned before any deductions from your paycheque. The four most common methods of employee remuneration include salaries, hourly wages, commissions, and piecework wages.

Salary and Hourly Wages

One ad in the employment classifieds indicates compensation of [latex]\$1,270[/latex] biweekly, while a similar competing ad promotes wages of [latex]\$1,400[/latex] semi-monthly. If both job ads are similar in every other way, which job has the higher annual gross earnings? To make this assessment, you must understand how salaries work. A salary is a fixed compensation paid to a person on a regular basis for services rendered. Most employers pay employees by salary in occupations where the employee’s work schedule generally remains constant.

In contrast, an hourly wage is a variable compensation based on the time an employee has worked. In contrast to a salary, this form of compensation generally appears in occupations where the number of hours is unpredictable or continually varies from period to period.

Employment Contract Characteristics

Salaried and hourly full-time employees are similar with regard to their gross earnings. The major earnings issues in an employment contract involve regular earnings structure, overtime, and holidays.

Regular Earnings Structure

An agreement with your employer outlines the terms of your employment, including the time frame and frequency of pay.

• Time Frame

For salaried employees, the time frame that the salary covers must be clearly stated. For example, you could receive a salary of [latex]\$2,000[/latex] monthly or [latex]\$50,000[/latex] annually. Notice that each of these salaries is followed by the specific time frame for the compensation. For hourly employees, the time frame requires identification of the wage earned per hour.

• Frequency

How often the gross earnings are paid out to the employee must be defined.

• • Monthly: Earnings are paid once per month. By law, employees must receive compensation from their employer at least once per month, which equals [latex]12[/latex] times per year.
  • Daily: Earnings are paid at the end of every day. This results in about [latex]260[/latex] paydays per year ([latex]5[/latex] days per week multiplied by [latex]52[/latex] weeks per year). In a leap year, there might be one additional payday.
  • Weekly: Earnings are paid once every week. This results in [latex]52[/latex] paydays in any given year since there are [latex]52[/latex] weeks per year.
  • Biweekly: Earnings are paid once every two weeks. This results in [latex]26[/latex] paydays in any given year since there are [latex]52\div 2=26[/latex] biweekly periods per year.
  • Semi-monthly: Earnings are paid twice a month, usually every half month (meaning on the [latex]15th[/latex] and last day of the month). This results in [latex]24[/latex] paydays per year.

Thus, the earnings structure specifies both the time frame and the frequency of earnings. For a salaried employee, this may appear as “[latex]\$2,000[/latex] monthly paid semi-monthly” or “[latex]\$50,000[/latex] annually paid biweekly.” For an hourly employee, this may appear as “[latex]\$10[/latex] per hour paid weekly.” No matter whether you are salaried or hourly, earnings determined by your regular rate of pay are called your regular earnings.

_{* Special thanks to Steven Van Alstine (CPM, CAE), Vice-President of Education, the Canadian Payroll Association, for assistance in summarizing Canadian payroll legislation and jurisdictions.}

Overtime

Overtime is work time in excess of your regular workday, regular workweek, or both. In most jurisdictions it is paid at [latex]1.5[/latex] times your regular hourly rate (called time-and-a-half), though your company may voluntarily pay more or a union may have negotiated a more favourable rate such as two times your regular hourly rate (called double time). A contract with an employer will specify your regular workday and workweek, and some occupations are exempt from overtime. Due to the diversity of occupations, there is no set rule on what constitutes a regular workday or workweek. In most jurisdictions, a regular workweek is eight hours per day and [latex]40[/latex] hours per week. Once you exceed these regular hours, you are eligible to receive overtime or premium earnings, which are based on your overtime rate of pay.

Holidays

A statutory holiday is a legislated day of rest with pay. Five statutory holidays are recognized throughout Canada, namely, New Year’s Day, Good Friday (or Easter Monday in Quebec), Canada Day, Labour Day, and Christmas Day. Each province or territory has an additional four to six public holidays (or general holidays), which may include Family Day (known as Louis Riel Day in Manitoba and Islander Day in PEI) in February, Victoria Day in May, the Civic Holiday in August, Thanksgiving Day in October, Remembrance Day in November, and Boxing Day in December. These public holidays may or may not be treated the same as statutory holidays, depending on provincial laws.

Statutory and public holidays generally require employees to receive the day off with pay. If the holiday falls on a nonworking day, it is usually the next working day that is given off instead. For example, if Christmas Day falls on a Saturday, typically the following Monday is given off with pay. Here’s how holidays generally work (though you should always consult legislation for your specific jurisdiction):

• You should be given the day off with pay, called holiday earnings. The holiday earnings are in the amount of a regular day’s earnings, and the hours involved count toward your weekly hourly totals for overtime purposes (preventing employers from shifting your work schedule that week).
• If you are required to work, the employer must offer another day off in lieu with pay. Your work on the statutory holiday is then paid at regular earnings and the hours involved contribute toward your weekly hourly totals for overtime purposes. You are paid holiday earnings on your future day off.
• If you are required to work and no day or rest is offered in lieu, this poses the most complex situation. Under these conditions:
• You are entitled to the holiday earnings you normally would have received for the day off. The hours that make up your holiday earnings contribute toward your weekly hourly totals for overtime purposes (again, consult your local jurisdiction).
• In addition, for the hours you worked on the statutory holiday you are entitled to overtime earnings known as statutory holiday worked earnings. These hours do not contribute toward your weekly hourly totals for overtime purposes since you are already compensated at a premium rate of pay. For example, assume you work eight hours on Labour Day, your normal day is eight hours, and you won’t get another day off in lieu. Your employer owes you the eight hours of holiday earnings you should have received for getting the day off plus the eight hours of statutory holiday worked earnings for working on Labour Day.

The four forms of compensation consist of regular earnings, overtime earnings, holiday earnings, and statutory holiday worked earnings. Add these four elements together to determine total gross earnings. Formula 3.3 shows the relationship.

[latex]\boxed{3.3}[/latex] Salary & Hourly Gross Earnings

[latex]{\color{Mahogany}{\text{Statutory Holiday Worked Earnings:}}}[/latex] This pay shows up only if a statutory holiday is worked and the employee will not receive another paid day off in lieu. It is received in addition to the holiday pay and must be paid at a premium rate

[latex]{\color{red}{\text{GE}}}\text{ is Gross Earnings:}[/latex] Gross earnings are earning before any deductions and represent the amount owed to the employee for services rendered. This is commonly called the gross amount of the paycheque.

[latex]{\color{purple}{\text{Holiday Earnings:}}}[/latex] If a statutory holiday occurs during a pay period, this is holiday pay in an amount that represents a regular shift.

[latex]{\color{blue}{\text{Regular Earnings:}}}[/latex] Unless the employees have exceeded their daily or weekly thresholds or a holiday is involved, all hours worked are considered regular earnings

[latex]{\color{green}{\text{Overtime Earnings:}}}[/latex] Any hours worked that exceed daily or weekly thresholds fall under overtime earnings. For most individuals, this is calculated at 1.5 times their regular hourly rate.

Paths To Success

In calculating the pay for a salaried employee, this textbook assumes for simplicity that a year has exactly [latex]52[/latex] weeks. In reality, there are [latex]52[/latex] weeks plus one day in any given year. In a leap year, there are [latex]52[/latex] weeks plus two days. This extra day or two has no impact on semi-monthly or monthly pay, since there are always [latex]24[/latex] semi-months and [latex]12[/latex] months in every year. However, weekly and biweekly earners are impacted as follows:

• If employees are paid weekly, approximately once every six years there are [latex]53[/latex] pay periods in a single year. This would “reduce” the employees’ weekly paycheque in that year. For example, assume they earn [latex]\$52,000[/latex] per year paid weekly. Normally, they are paid [latex]\$52,000\div 52=\$1,000\;\text{per week}[/latex]. However, since there are [latex]53[/latex] pay periods approximately every sixth year, this results in [latex]\$52,000\div 53=\$981.13\;\text{per week}[/latex] for that year.
• If employees are paid biweekly, approximately once every [latex]12[/latex] years there are [latex]27[/latex] pay periods in a single year. This has the same effect as the extra pay period above. For example, if they are paid [latex]\$52,000[/latex] per year biweekly they normally receive [latex]\$52,000\div 26=\$2,000[/latex] per biweekly cheque. Approximately every twelfth year, they are paid [latex]\$52,000\div 27=\$1,925.93[/latex] per biweekly cheque for that year.

Many employers ignore these technical nuances in pay structure since the extra costs incurred to modify payroll combined with the effort required to calm down employees who don’t understand the smaller paycheque are not worth the savings in labour. Therefore, most employers treat every year as if it has [latex]52[/latex] weeks ([latex]26[/latex] biweeks) regardless of the reality. In essence, employees receive a bonus paycheque approximately once every six or twelve years!

Example 3.3.2

Marcia receives an hourly wage of [latex]\$32.16[/latex] working on an automotive production line. Her union has negotiated a regular work day of [latex]7.25\;\text{hours}[/latex] for five days totaling [latex]36.25\;\text{hours}[/latex] for the week. Overtime is paid at [latex]1.5[/latex] times her regular rate for any work that exceeds the daily or weekly limits. If work is required on a statutory holiday, her company does not give a day off in lieu and pays a premium rate of [latex]2.5[/latex] times her regular rate. Last week, Marcia worked nine hours on Monday, her regular hours on Tuesday through Friday inclusive, and three hours on Saturday. Friday was a statutory holiday. Calculate Marcia’s gross earnings for the week.

Solution

Step 1: What are you looking for?

You need to calculate Marcia’s gross earnings, or [latex]\text{GE}[/latex], for the week.

Step 2: What do you already know?

Step 1: You know Marcia’s pay structure and workweek:

[latex]\begin{align*}\text{Regular Hourly Rate}&=\$32.16\\\text{Overtime Hourly Pay}&=\times 1.5\\\text{Statutory Holiday Worked Rate}&=\times 2.5\end{align*}[/latex]

Exceeding [latex]7.25\;\text{hours}[/latex] daily or [latex]36.25\;\text{hours}[/latex] weekly is overtime.

Table 3.3.2

Sunday	0
Monday	9
Tuesday	7.25
Wednesday	7.25
Thursday	7.25
Friday (statutory holiday)	7.25
Saturday	3

Step 3: Make substitutions using the information known above.

Take Marcia’s hours and place them into the table. Assess whether any daily or weekly totals are considered overtime and make any necessary adjustments.

Table 3.3.3

Type	Sun	Mon	Tue	Wed	Thu	Fri	Sat	Total	Rate	Earnings
Regular	0	7.25	7.25	7.25	7.25		3	39.25	$32.16
Holiday						7.25
Overtime		1.75						1.75
Holiday Worked						7.25		7.25
								TOTAL EARNINGS

She worked nine hours. Therefore, the first [latex]7.25\;\text{hours}[/latex] are regular pay and the last [latex]1.75[/latex] are overtime pay.

Friday was a statutory holiday, and she will not receive another day off in lieu. She must receive statutory holiday worked pay in addition to her hours worked.

Note the weekly total of [latex]36.25[/latex] has been exceeded by three hours. Move Saturday’s hours into overtime.

The following table is the final layout of her workweek:

Table 3.3.4

Type	Sun	Mon	Tue	Wed	Thu	Fri	Sat	Total	Rate	Earnings
Regular	0	7.25	7.25	7.25	7.25			36.25	$32.16
Holiday						7.25
Overtime		1.75					3	4.75
Holiday Worked						7.25		7.25
								TOTAL EARNINGS

Perform necessary calculations to obtain her Gross Earnings using Formula 3.3[latex]\small\text{GE}=\text{Regular}+\text{OT}+\text{Holiday}+\text{Stat Worked}[/latex].

[latex]\begin{align*}\text{Holiday Earnings }&=7.25\times\$32.16\\\text{Holiday Earnings }&=\$233.16\end{align*}[/latex]

[latex]\begin{align*}\text{Overtime Hourly Rate}&=\$32.16\times 1.5\\\text{Overtime Hourly Rate}&=\$48.24\end{align*}[/latex]

[latex]\begin{align*}\text{Overtime Earnings}&=4.75\times\$48.24\\\text{Overtime Earnings}&=\$229.14\end{align*}[/latex]

[latex]\begin{align*}\text{Statutory Holiday Worked Rate}&=\$32.16\times 2.5\\\text{Statutory Holiday Worked Rate}&=\$80.40\end{align*}[/latex]

[latex]\begin{align*}\text{Statutory Worked Earnings}&=7.25\times\$80.40\\\text{Statutory Worked Earnings}&=\$582.90\end{align*}[/latex]

[latex]\begin{align*}\text{Regular Earnings}&=29\times\$32.16\\\text{Regular Earnings}&= \$932.64\end{align*}[/latex]

[latex]\begin{align*}\text{GE}&=\$932.64+\$229.14+\$233.16+\$582.90\\\text{GE}&=\$1,977.84\end{align*}[/latex]

Table 3.3.5

Type	Sun	Mon	Tue	Wed	Thu	Fri	Sat	Total	Rate	Earnings
Regular	0	7.25	7.25	7.25	7.25			36.25	$32.16	$932.64
Holiday						7.25				$233.16
Overtime		1.75					3	4.75	$48.24	$229.14
Holiday Worked						7.25		7.25	$80.40	$582.90
								TOTAL EARNINGS		$1,977.84

Step 4: Provide the information in a worded statement.

Marcia will receive total gross earnings of [latex]\$1,977.84[/latex] for the week.

Commission

Over the last two weeks you sold [latex]\$50,000[/latex] worth of machinery as a sales representative for IKON Office Solutions Canada. IKON’s compensation plan involves a straight commission rate of [latex]3.5\%[/latex]. What are your gross earnings? If you sold an additional [latex]\$12,000[/latex] in machinery, how much more would you earn?

Particularly in the fields of marketing and customer service, many workers are paid on a commission basis. A commission is an amount or a fee paid to an employee for performing or completing some form of transaction. The commission typically takes the form of a percentage of the dollar amount of the transaction. Marketing and customer service industries use this form of compensation as an incentive to perform: If the representative doesn’t sell anything then the representative does not get paid. Issues to be discussed about commission include what constitutes regular earnings, how to handle holidays and overtime, and the three different types of commission structures.

• Regular Earnings. All commissions are considered to be regular earnings. To calculate the gross earnings for an employee, take the total amount of the transactions and multiply it by the commission rate:

  [latex]\text{Gross Earnings}=\text{Total Transaction Amount}\times\text{Commission Rate}[/latex]

  This is not a new formula. It is a specific application of Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex]: Rate, Portion, Base. In this case, the Base is the total amount of the transactions, the Rate is the commission rate, and the Portion is the gross earnings for the employee.

• Holidays and Overtime. Commission earners are eligible to receive overtime earnings, holiday earnings, and statutory holiday worked earnings. However, the provincial standards on these matters vary widely and the mathematics involved do not necessarily follow any one procedure or calculation. As such, this textbook leaves these issues to be covered in a payroll administration course.
• Types of Commission. Commission earnings typically follow one of the following three structures:
  • Straight Commission. If your entire earnings are based on your dollar transactions and calculated strictly as a percentage of the total, you are on straight commission. An application of Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex] (Rate, Portion, Base) calculates your gross earnings under this structure.
  • Graduated Commission. Within a graduated commission structure, you are offered increasing rates of commission for higher levels of performance. The theory behind this method of compensation is that the higher rewards motivate employees to perform better. An example of a graduated commission scale is found in the table below.

    Table 3.3.6

    Transaction Level	Commission Rate
    $0–$100,000.00	3%
    $100,000.01–$250,000.00	4.5%
    $250,000.01–$500,000.00	6%
    Over $500,000.00	7.5%

    Recognize that the commission rates are applied against the portion of the sales falling strictly into the particular category, not the entire balance. Thus, if the total sales equal [latex]\$150,000[/latex], then the first [latex]\$100,000[/latex] is paid at [latex]3\%[/latex] while the next [latex]\$50,000[/latex] is paid at [latex]4.5\%[/latex].

  • Salary Plus Commission. If your earnings combine a basic salary together with commissions on your dollar transactions, you have a salary plus commission structure. No new mathematics are required for this commission type. You must combine salary calculations, discussed earlier in this section, with either a straight commission or graduated commission, as discussed above. Usually this form of compensation pays the lowest commission rate since a basic salary is already provided.

HOW TO

Calculate Commission Earnings

Follow these steps to calculate commission earnings:

Step 1: Determine which commission structure is used to pay the employee. Identify information on commission rates, graduated scales, and any salary.

Step 2: Determine the dollar amounts that are eligible for any particular commission rate and calculate commissions.

Step 3: Sum all earnings from every eligible commission rate plus any salary.

Table 3.3.7 Data Table for Figure 3.3.2

Commission Scale Amount Earned 3% $3,000 4.5% $6,750 6% $7,800 Total $17,550

Let’s assume [latex]\$380,000[/latex] of merchandise is sold. Using the previous table as our graduated commission scale, calculate commission earnings.

Step 1: Sales total [latex]\$380,000[/latex] and all commission rates and scales are found in the table.

Step 2: The first [latex]\$100,000[/latex] is compensated at [latex]3\%[/latex], equaling [latex]\$3,000[/latex]. The next [latex]\$150,000[/latex] is compensated at [latex]4.5\%[/latex], equaling [latex]\$6,750[/latex]. The last [latex]\$130,000[/latex] is compensated at [latex]6\%[/latex], equaling [latex]\$7,800[/latex]. There is no compensation at the [latex]7.5\%[/latex] level since sales did not exceed [latex]\$500,000[/latex].

Step 3: The total commission on sales of [latex]\$380,000[/latex] is [latex]\$3,000+\$6,750+\$7,800=\$17,550[/latex].

Example 3.3.3

Josephine is a sales representative for Kraft Foods Canada. Over the past two weeks, she closed [latex]\$325,000[/latex] in retail distribution contracts. Calculate the total gross earnings that Josephine earns if

1. She is paid a straight commission of [latex]3.45\%[/latex].
2. She is paid [latex]2\%[/latex] for sales on the first [latex]\$100,000[/latex], [latex]3\%[/latex] on the next [latex]\$100,000[/latex], and [latex]4\%[/latex] on all remaining sales.
3. She is paid a base salary of [latex]\$2,000[/latex] plus a commission of [latex]3.5\%[/latex] on all sales above [latex]\$100,000[/latex].

Solution

Step 1: What are we looking for?

You need to calculate the gross earnings, or [latex]\text{GE}[/latex], for Josephine under various commission structures.

Step 2: What do we already know?

For all three options, [latex]\text{total sales}=\$325,000[/latex]

a. This is a straight commission where [latex]\text{Commission Rate=3.45}\%[/latex].

b. This is a graduated commission, structured as follows:

Table 3.3.8

Sales Level	Rate
[latex]\$0\text{-}\$100,000.00[/latex]	[latex]2\%[/latex]
[latex]\$100,000.01\text{-}\$200,000.00[/latex]	[latex]3\%[/latex]
[latex]\$200,000.01\;\text{and above}[/latex]	[latex]4\%[/latex]

c. This is a salary plus graduated commission, with [latex]\text{ Base Salary}=\$2,000[/latex] and a graduated commission structure as follows:

Table 3.3.9

Sales Level	Rate
[latex]\$0\text{-}\$100,000.00[/latex]	[latex]0\%[/latex]
[latex]\$100,000.01\;\text{and above}[/latex]	[latex]3.5\%[/latex]

Step 3: Make substitutions using the information known above.

Determine the sales eligible for each commission and calculate total commissions, then sum all commissions plus any salary to calculate total gross earnings.

a.

[latex]\begin{align*}\text{Total Gross Earnings}&=\text{Rate}\times\text{Base}\\\text{Total Gross Earnings}&=3.45\%\times\$325,000\\\text{Total Gross Earnings}&=0.0345\times\$325,000\\\text{Total Gross Earnings}&=\$11,212.50\end{align*}[/latex]

b.

Table 3.3.10

Sales Level	Rate	Eligible Sales at Each Rate (Base)	Commission Earned ([latex]\text{Rate}\times\text{Base}[/latex])
[latex]\$0\text{–}\$100,000.00[/latex]	[latex]2\%[/latex]	[latex]\Large{\$100,000-\$0\\=\$100,000}[/latex]	[latex]\Large{0.02\times\$100,000\\=\$2,000}[/latex]
[latex]\$100,000.01\text{–}\$200,000.00[/latex]	[latex]3\%[/latex]	[latex]\Large{\$200,000-\$100,000\\=\$100,000}[/latex]	[latex]\Large{0.03\times\$100,000\\=\$3,000}[/latex]
[latex]\$200,000.01\;\text{and above}[/latex]	[latex]4\%[/latex]	[latex]\Large{\$325,000–\$200,000\\=\$125,000}[/latex]	[latex]\Large{0.04\times\$125,000\\=\$5,000}[/latex]

[latex]\begin{align*}\text{Total Gross Earnings}&=\$2,000+\$3,000+\$5,000\\\text{Total Gross Earnings}&=\$10,000\end{align*}[/latex]

c. Recall [latex]\text{Base Salary}=\$2,000[/latex]

Table 3.3.11

Sales Level	Rate>	Base	Commission Earned ([latex]\text{Rate}\times\text{Base}[/latex])
[latex]\$0\text{–}\$100,000.00[/latex]	[latex]0\%[/latex]	[latex]\Large{\$100,000−\$0\\=\$100,000}[/latex]	[latex]\Large{0\times\$100,000\\=\$0}[/latex]
[latex]\$100,000.01\;\text{and above}[/latex]	[latex]3.5\%[/latex]	[latex]\Large{\$325,000–\$100,000\\=\$225,000}[/latex]	[latex]\Large{0.035\times\$225,000\\=\$7,875}[/latex]

[latex]\begin{align*}\text{Total Gross Earnings}&=\$0+\$7,875+\$2,000\\\text{Total Gross Earnings}&=\$9,875\end{align*}[/latex]

Step 4: Provide the information in a worded statement.

If Josephine is paid under straight commission, her total gross earnings will be [latex]\$11,212.50[/latex]. Under the graduated commission, she will receive [latex]\$10,000[/latex] in total gross earnings. For the salary plus commission, she will receive [latex]\$9,875[/latex] in total gross earnings.

Piecework

Have you ever heard the phrase “pay-for-performance”? Although this phrase has many interpretations in different industries, for some people this phrase means that they get paid based on the quantity of work that they do. For example, many workers in clothing manufacturing are paid a flat rate for each article of clothing they produce. As another example, employees in fruit orchards may get paid by the number of pieces of fruit that they harvest, or simply by the kilogram. As you can see, these workers are neither salaried nor paid hourly, nor are they on commission. They earn their paycheque for performing a specific task. Therefore, a piecework wage compensates such employees on a per-unit basis.

This section focuses on the regular earnings only for piecework wage earners. Similar to workers on commission, piecework earners are eligible to receive overtime earnings, holiday earnings, and statutory holiday worked earnings. However, the standards vary widely from province to province, and there is not necessarily any one formula to calculate these earnings. As with commissions, this textbook leaves those calculations for a payroll administration course.

To calculate the regular gross earnings for a worker paid on a piecework wage, you require the piecework rate and how many units they are to be paid for:

[latex]\text{Gross Earnings}=\text{Piecework Rate}\times\text{Eligible Units}[/latex]

This is not a new formula but another application of Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex] (Rate, Portion, Base). The [latex]\text{Piecework Rate}[/latex] is the [latex]\text{Rate}[/latex], the [latex]\text{Eligible Units}[/latex] are the [latex]\text{Base}[/latex], and the [latex]\text{Gross Earnings}[/latex] are the [latex]\text{Portion}[/latex].

Assume that Juanita is a piecework earner at a blue jean manufacturer. She is paid daily and earns [latex]\$1.25[/latex] for every pair of jeans that she sews. On a given day, Juanita sewed [latex]93[/latex] pairs of jeans. Her gross earnings are calculated as follows:

Step 1: Her [latex]\text{Piecework Rate}=\$1.25\;\text{per pair}[/latex] with production of [latex]93\;\text{units}[/latex].

Step 2: The rate and production are both expressed by the pair of jeans. No modification is necessary.

Step 3: Her gross piecework earnings are the product of the rate and units produced, or [latex]\$1.25\times 93=\$116.25[/latex].

Section 3.3 Exercises