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A1.4 · Solve problems comparing remuneration methods and schedules

Learn to solve problems comparing remuneration methods and schedules through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Earning and Purchasing

MEL3E workplace mathematics: expectation A1.4

Two jobs can advertise different pay arrangements. One might pay by the hour, while another pays a fixed amount each week. Even when the total pay is similar, the dates when money arrives can differ. To compare offers fairly, identify how each job calculates pay and how often it pays. Then compare amounts over the same time period. In this lesson, gross pay means earnings before any deductions are taken off. The examples use gross pay because that is the amount being compared.

What you will learn

Explain the difference between a remuneration method and a pay schedule.
Calculate and compare gross pay using information from a workplace offer or pay record.
Use repeated calculations, a calculator, or a spreadsheet to compare pay over the same length of time.
Choose a pay arrangement that suits a stated need and explain the choice.

1. Separate the pay method from the pay schedule

A remuneration method is the way a workplace calculates what a worker earns. Common methods include hourly pay, a fixed salary, commission, and piecework. With hourly pay, earnings depend on hours worked and the hourly rate. A salary is a set amount for a stated period, such as a week or a year. Commission is pay based on sales, often calculated as a percentage of sales. Piecework pays an amount for each item or task completed.

A pay schedule tells you when pay is issued. For example, a workplace might pay every week, every two weeks, or twice each month. These schedules are not identical: two payments each month do not always mean one payment every two weeks. The schedule affects the size and timing of each paycheque, but by itself it does not tell you how much you earn over a year.

Start by reading the details carefully. Look for the rate, the time period, the expected hours or sales, and the pay schedule. If a job states a weekly salary, do not treat that amount as an hourly rate. If a commission offer gives a percentage, find out what sales amount the percentage applies to.

Method means how earnings are calculated.
Schedule means how often pay is issued.
Compare pay over the same time period.

2. Calculate earnings with repeated steps

For hourly pay, multiply the hourly rate by the number of hours worked. For commission, multiply the sales amount by the commission rate written as a decimal. For example, a commission of 5% is the same as 0.05. For piecework, multiply the number of completed items by the amount paid for each item. A salary may already give the pay for a week or another stated period.

A calculator is useful for checking multiplication and adding pay across several weeks. A spreadsheet can make comparisons easier when hours or sales change from week to week. Enter one week per row, calculate that week's pay, and add the weekly amounts. Keep the units clear: dollars per hour multiplied by hours gives dollars.

When a pay schedule is less frequent than the work period in your records, add the earnings for all the weeks covered by that paycheque. For example, a two-week pay period combines the earnings from two weeks. Do not multiply a weekly amount by the number of pay periods unless each pay period represents exactly one week.

\text{hourly earnings} = \text{hourly rate} \times \text{hours worked}

Hourly pay: rate multiplied by hours.
Commission: sales multiplied by commission rate.
Piecework: completed items multiplied by pay per item.
Add matching periods before comparing totals.

3. Make a fair comparison

A fair comparison uses the same number of weeks or months for each option. If one offer lists weekly pay and another lists pay every two weeks, calculate or add the earnings for the same two-week span. If an offer gives an annual salary and another gives hourly pay, first work out the hourly job's earnings using the expected hours and weeks. State any assumptions, such as working the same number of hours each week.

A table helps keep the details organized. Record the method, the amount earned in one week, and the pay schedule. Then compare the totals for the period that matters to you. A larger paycheque may simply cover more weeks; it does not necessarily mean the job pays more overall.

Pay timing can matter even when total earnings match. A person with regular bills may prefer money arriving more often, while another may prefer a less frequent schedule. The calculations show the amounts and dates stated in the offers. They do not decide which arrangement is best for everyone.

Use the same comparison period for every option.
Check whether a pay amount covers one week, two weeks, or another period.
Use the stated work hours, sales, or output, and name your assumptions.

4. Use the results to make a decision

After calculating, explain your decision in plain language. You might say that one offer gives more gross pay over two weeks, or that both offers give the same total but use different schedules. If the result depends on variable hours, sales, or completed items, point that out. A comparison based on estimated sales is not a promise that those sales will happen.

A practical check is to calculate each option a second way, such as adding weekly totals instead of multiplying a weekly amount. Check that the comparison covers the same number of weeks and that a percentage was entered correctly. These checks help catch common errors before you rely on the result.

Report the comparison period and the gross-pay totals.
Explain how variable work could change the result.
A schedule changes when money arrives, not necessarily the total earned.

Keep method, amount, and schedule distinct

Offer	Pay method	Gross pay for two weeks	Pay schedule
Café	Hourly	CAD 864	Weekly
Garden centre	Hourly	CAD 884	Every two weeks
Fixed-pay shop	Fixed weekly amount	CAD 920	Weekly
Commission shop	6% of sales	CAD 504 at stated sales	Every two weeks

Worked example

Example 1: Hourly pay on different schedules

A café offers CAD 18 per hour for 24 hours each week and pays weekly. A garden centre offers CAD 17 per hour for 26 hours each week and pays every two weeks. Compare the gross pay from each job over two weeks.

Find each weekly amount
Multiply each hourly rate by its weekly hours. This gives the gross pay for one week at each job.
$18 \times 24 = 432;\quad 17 \times 26 = 442$
Use the same two-week period
The café pays weekly, so add two weekly amounts. The garden centre's stated two-week pay covers both weeks, so double its weekly amount as well.
$432 + 432 = 864;\quad 442 + 442 = 884$
Compare the totals
Subtract the smaller two-week total from the larger one. This shows the difference in gross pay for the same length of time.
$884 - 864 = 20$

Answer: Over two weeks, the café pays CAD 864 gross and the garden centre pays CAD 884 gross. The garden centre pays CAD 20 more for that period. Its paycheque arrives every two weeks, while the café issues pay weekly.

Check: The weekly amounts are CAD 432 and CAD 442. Adding each amount twice gives CAD 864 and CAD 884, so the two-week comparison is consistent.

Worked example

Example 2: Fixed weekly pay or sales commission

A shop offers a fixed CAD 460 per week, paid weekly. Another shop offers commission of 6% of sales, paid every two weeks. A worker expects sales of CAD 3,900 in one week and CAD 4,500 in the next. Compare gross pay over those two weeks, assuming the commission applies to all sales.

Find the fixed-pay total
The fixed offer pays CAD 460 each week. Add two weeks because the comparison covers two weeks.
$460 + 460 = 920$
Add the two weeks of sales
Commission is based on sales, so first combine the sales amounts for the full two-week period.
$3{,}900 + 4{,}500 = 8{,}400$
Calculate commission
Convert 6% to 0.06, then multiply the two-week sales total by that rate. The result is the commission for the comparison period.
$8{,}400 \times 0.06 = 504$
Compare and consider uncertainty
Compare the two-week totals. The commission offer pays less at these sales amounts, but its result changes when sales change.
$920 - 504 = 416$

Answer: The fixed-pay offer gives CAD 920 gross over two weeks. The commission offer gives CAD 504 gross based on the expected sales, which is CAD 416 less. The fixed offer also pays weekly, while the commission offer pays every two weeks.

Check: Six percent of CAD 8,400 is CAD 504. The sales total and the fixed-pay total both cover two weeks, so the comparison period matches.

Common mistakes and how to avoid them

Comparing one week's pay from one offer with two weeks of pay from another.

Correction: Convert both amounts to the same number of weeks before deciding which is larger.

Treating a pay schedule as if it changes the amount earned.

Correction: The schedule tells you when pay arrives. Calculate the earnings separately using the method and work details.

Using 6 as the multiplier for a 6% commission.

Correction: Convert the percentage to a decimal: 6% is 0.06.

Assuming estimated commission is guaranteed.

Correction: Commission depends on actual sales. Label a calculation as an estimate when sales are expected rather than known.

Lesson summary

A remuneration method explains how earnings are calculated; a pay schedule explains when they are paid.
Use the rate and work details to calculate earnings, then add matching periods.
Compare gross pay over the same length of time and state assumptions about variable work.
Pay frequency can affect cash timing even when total earnings are alike.

Check your understanding

Question 1

A worker earns CAD 16 per hour for 20 hours each week. What is the gross pay for two weeks?

CAD 320
CAD 640
CAD 720
CAD 1,600

Show answer and explanation

CAD 640

One week is 16 times 20, or CAD 320. Two weeks total CAD 640.

Question 2

A worker earns 5% commission on CAD 2,000 in sales. What is the commission?

CAD 10
CAD 100
CAD 500
CAD 1,000

Show answer and explanation

CAD 100

Five percent is 0.05. Multiplying CAD 2,000 by 0.05 gives CAD 100.

Question 3

What information does a pay schedule give?

How often pay is issued
How many sales a worker will make
The hourly rate in every job
The amount of deductions from pay

Show answer and explanation

How often pay is issued

A pay schedule tells when or how often pay is issued. It does not set sales, rates, or deductions.

Key terms

Remuneration method: The way a workplace calculates what a worker earns.
Pay schedule: How often and when a workplace issues pay.
Gross pay: Earnings before deductions are taken off.
Commission: Pay calculated from sales, often as a percentage.
Piecework: Pay based on the number of items or tasks completed.
Assumption: A detail treated as true for a calculation, such as the same work hours each week.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation A1.4. It is a study resource, not an official curriculum publication.

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