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Math · Consumer Math

Chapter 1: Earning an Income

Wages, Salary, and Gross Pay

What the job actually pays.

Lesson
1
Time
About 20 minutes
0 of 23 done
Part 1 of 7Let's Learn

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Try it first

Lena earns $10 an hour for her first 40 hours in a week. Every hour after that pays $15. This week she worked 42 hours. How much did she earn, in dollars?

dollars

Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.

Watch the idea first — 57 seconds. Then read on, and try it yourself in the next step.

$20 an hour, 46 hours this week. Gross pay?

  1. 140 × 20 = $800the first 40 hours at the normal rate
  2. 26 overtime hours at 1.5 × 20 = $30time and a half
  3. 36 × 30 = $180the overtime
  4. Answer800 + 180 = $980 grossresult

Hourly pay multiplies a rate by hours worked. A salary is a fixed annual amount, paid in equal instalments. Hours beyond 40 in a week are commonly paid at 1.5 times the normal rate. Commission pays a percentage of sales. Everything here is gross pay, before deductions.

A salary, per period

$52,000 a year is 52,000/12 = $4,333 a month, or 52,000/26 = $2,000 a fortnight, or 52,000/52 = $1,000 a week. Divide by the number of pay periods in the year.

Comparing offers

To compare a salary with an hourly rate, convert both to the same period. A full-time year is about 2080 hours: $52,000 a year is 52,000/2080 = $25 an hour. $26 an hour is 26 × 2080 = $54,080 a year.

Commission

A base of $2,000 a month plus 3% of sales. With $40,000 of sales: 2,000 + 0.03 × 40,000 = 2,000 + 1,200 = $3,200. Commission alone at 8% on $40,000 would be $3,200 too, but with no floor in a slow month.

Overtime, in general

Overtime pay = (hours − 40) × 1.5 × rate. At $18 an hour for 50 hours: 40 × 18 + 10 × 27 = 720 + 270 = $990. The overtime rate is found once, then multiplied by the extra hours.

Gross is not what arrives

Everything computed here is gross pay. The amount reaching your account is net pay, after taxes and other deductions, and it is always less: commonly a fifth to a third less.

A sanity check

46 hours at $20 would be $920 with no overtime. The overtime adds 6 × $10 extra, $60, giving $980. Compute the plain total first; the overtime premium is the difference.

Step 2: Try It Yourself

Tap and try it out.

Press Next step. Everything to the same period, then compare.

Offer A: $52,000 a year. Offer B: $26 an hour, 40 hours a week. Offer C: $1,500 a month plus 5% of $30,000 monthly sales. Compare per year

  1. 1A: $52,000; per hour 52,000/2080 = $25a full-time year is about 2080 hours
Step 0 of 4
A week of hours at a rate. Past 40, each hour pays time and a half.
Gross pay this week$980
  • 40 hours at $20$800
  • 6 overtime hours at $30$180

40 hours at $20 is $800, plus 6 overtime hours at $30 is $180. Gross pay $980.

Past 40 hours, each hour pays 1.5 times the rate: time and a half. This is gross pay. What reaches the account is less.

Step 3: In Real Life

A first paycheck

16 dollars an hour, 35 hours a week, plus 5 hours at time and a half: 560 + 120 = 680 gross. Every pay stub starts with this line.

Step 4: Watch an Example

One step at a time.

Watch Amara Work Out a Week With Overtime

Amara earns $17 an hour. This week she worked 45 hours, and her job pays time and a half after 40.

  1. Step 1

    The week splits in two. The first 40 hours are paid at the normal rate: 40 × $17 = $680. That leaves 45 − 40 = 5 hours of overtime.

Watch Leo Work Out a Long Week

Leo earns $14 an hour and worked 48 hours, with time and a half after 40. He writes the first line, and you write the rest.

  1. Step 1

    The first 40 hours pay the normal rate: 40 × $14 = $560. That leaves 48 − 40 = 8 hours of overtime.

Watch Noor Compare Two Offers

Noor has two job offers. One pays a salary of $45,760 a year. The other pays $21.50 an hour, full time.

  1. Step 1

    One number is per year and the other is per hour. Two different periods, so 45,760 and 21.50 cannot be compared as they stand.

Step 5: Your Turn

Practice makes it stick.

The Phone Store

Problem 1 of 17

Marco sells phones. He earns a base of $1,600 a month plus 4% of his sales. In June he sold $25,000 of phones. What was his gross pay for June, in dollars?

dollars

The First Paycheck

Problem 2 of 17

Tess takes a job with a salary of $50,400 a year, paid monthly. How much is each paycheck before deductions, in dollars?

dollars

Work Out the Pay

Hourly, overtime, salary or commission. Name the kind of pay first, then work it out.

Problem 3 of 17

Jada works 32 hours at $15 an hour. What is her gross pay, in dollars?

dollars

Problem 4 of 17

A salary of $57,200 a year is paid weekly. How much is each weekly paycheck before deductions, in dollars?

dollars

Problem 5 of 17

Omar earns $22 an hour and worked 43 hours, with time and a half after 40. What is his gross pay, in dollars?

dollars

Problem 6 of 17

Rae earns a base of $1,500 a month plus 6% of her sales. This month she sold $20,000. What is her gross pay for the month, in dollars?

dollars

Problem 7 of 17

A job pays $46,800 a year. Using a 2080-hour full-time year, what does it pay per hour? Give the answer in dollars, to the cent.

dollars an hour

Whose Step?

One line in each page is a slip. Find it, then fix it.

Problem 8 of 17

Priya earns $18 an hour and worked 44 hours, with time and a half after 40. One line of her working is a slip. Which?

Priya's gross pay for 44 hours at $18

  1. 140 × 18 = $720
  2. 21.5 × 18 = $27
  3. 344 × 27 = $1,188
  4. Answer720 + 1,188 = $1,908

Problem 9 of 17

Fix Priya's working. What is her gross pay for the week, in dollars?

dollars

Problem 10 of 17

Dev has a salary of $36,400 a year, paid every two weeks. He worked out his paycheck. One line is a slip. Which?

Dev's paycheck on $36,400 a year, paid every two weeks

  1. 1$36,400 a year, paid every two weeks
  2. 252 ÷ 2 = 26 paychecks a year
  3. 336,400 ÷ 52 = $700
  4. Answer$700 each paycheck

Problem 11 of 17

Fix Dev's working. How much is each of his paychecks before deductions, in dollars?

dollars

Problem 12 of 17

Maya earns a base of $1,800 a month plus 5% of her sales. She sold $24,000 this month. One line of her working is a slip. Which?

Maya's gross pay: $1,800 base plus 5% of $24,000

  1. 1$1,800 base + 5% of $24,000
  2. 25% = 0.5
  3. 30.5 × 24,000 = $12,000
  4. Answer1,800 + 12,000 = $13,800

Problem 13 of 17

Fix Maya's working. What is her gross pay for the month, in dollars?

dollars

Pick the Move

Decide how to work it out before you do any arithmetic.

Problem 14 of 17

Ana is offered $49,920 a year at one job and $23 an hour, full time, at another. What should she do first to compare them?

Problem 15 of 17

Sam worked 47 hours at $20 an hour, with time and a half after 40. Which calculation gives his gross pay?

Same Pay?

Which of these pay the same? Convert to one period before you judge.

Problem 16 of 17

Select every way of being paid that comes to the same as $41,600 a year. Hourly pay is full time, 2080 hours a year.

Problem 17 of 17

Select every week that pays exactly $920 gross. Every job pays time and a half after 40 hours.

Step 6: Quick Check

Show what you know.

Question 1 of 2

25 hours at $16 an hour. Gross pay in dollars?

Question 2 of 2

What is the difference between gross and net pay?

Ready for more?Optional. Past the lesson, for anyone who wants it.

Stretch 1 of 2

Rosa earns $20 an hour, with time and a half after 40 hours. She wants to earn $1,100 gross this week. How many hours must she work in total?

hours

Stretch 2 of 2

Job A pays a salary of $2,400 a month. Job B pays a base of $1,200 a month plus 6% of sales. How much would you need to sell in a month for the two jobs to pay exactly the same, in dollars?

dollars

What You Learned

  • Hourly pay is rate times hours; a salary is a fixed annual amount divided by the pay periods.
  • Overtime beyond 40 hours is commonly 1.5 times the normal rate on the extra hours only.
  • Convert every offer to the same period before comparing; a year is about 2080 hours.
  • Everything here is gross pay, before deductions.
For the grown-up

The misconception this lesson targets is that time and a half applies to the whole week once it passes 40 hours, or that the overtime hours are added on top of a full week paid at the plain rate. Overtime is paid once, at 1.5 times the rate, on the hours past 40 only; the first 40 are paid at the normal rate. Two smaller slips ride alongside it: dividing a salary by the wrong number of pay periods (52 weeks where there are 26 two-week paychecks, or treating a month as exactly four weeks, when it is about 4.33), and reading a percent such as 5% as 0.5 instead of 0.05. The habit that catches all three is a sanity check: for overtime, the plain rate times all the hours plus the overtime premium gives the same total; for a salary, the paycheck times the number of paychecks gives back the salary; for commission, the result should be a small share of sales, not half of them.