Question

16. Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.

a. If both of them get $4.50 an hour, write an inequality to compare Peter’s and Cindy’s earnings.

b. What should Cindy’s per-hour income be so that she earns at least $14 a day? Write an inequality and an explanation of how to solve it.

Answer 1

Answer:

Part A)

• 4.50 × 3 > 4.50 × 2
• 13.5 0 > 9

Part B)

• r ≥ 7

Explanation:

1) The earnings are calculated multiplying the number of hours by the hourly rate.

2) The hourly rate of both Peter and Cindy is the same: $ 4.50 / hour

3) Let the variable used for computing the number of hours be h.

4) The number of hours Peter works every day is 3 hours, so, using the letter P to name Peter's earnings, the expression to calculate his earnings is:

• P = 4.50 × 3

5) Similarly, the expression to calculate Cindy's earnings would be:

• C = 4.50 × 2

Answering part A)

You have to write an inequality to compare Peter's and Cindy's earnings:

• 4.50 × 3 > 4.50 × 2
• 13.5 0 > 9

This is, the earnings of Peter are greater than the earnings of Cindy.

Part B),

You have to write an inequality to calculate Cindy's per-hour income so that she earns at least $ 14 a day.

• Here, C ≥ 14, because the sign ≥ means greater than or equal to, meaning the the earnings are greater than or equal to 14.

• Thus, since she works 2 hours per day, the inequality becomes 2 × r ≥ $ 14, where r is the per-hour income.

• To solve it follow these steps:

Given: 2r ≥ 14

Divide both sides by 2: r ≥ 14 / 2

Simplify: r ≥ 7

That means that Cindy's per-hour income should be at least $7 and hour so that she earns $14 a day.