Question

Working her way through school, Liz works two part-time jobs for a total of 28 hours a week. Job A pays $6.00 per hour, and Job B pays $6.60 per hour. How many hours did she work at each job the week that she made $175.80? (Round to two decimal places if necessary.)​

Answer 1

• A: 15 hours
• B: 13 hours

Explanation:

You want to know the number of hours Liz worked at each job, when the total pay for a total of 28 hours work was $175.80. Job A paid $6 per hour, and job B paid $6.60 per hour.

Setup

We can let 'b' represent the number of hours worked at job B. Then (28-b) is the number of hours worked at job A. Liz's total pay was ...

6(28 -b) +6.60(b) = 175.80

Solution

Simplifying the equation gives ...

0.60b +168.00 = 175.80

0.60b = 7.80 . . . . . . . . . . . subtract 168

b = 13 . . . . . . . . . . . . . . divide by 0.6

28-b = 28-13 = 15 . . . hours at Job A

Liz worked 15 hours at Job A, and 13 hours at Job B.

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Additional comment

Here, we used one equation. If you use two equations, you can get this same equation by substituting for the variable representing hours at Job A. Letting the variable represent hours at the higher-paying job generally results in arithmetic using positive numbers. If you write the equation for the hours at Job A, negative numbers will usually be involved. Though it shouldn't, sometimes that causes confusion.

A graphing calculator may offer two or three ways (or more) you use to can solve the equations. One of them is illustrated in the attachment. It solves the equations ...

• a + b = 28 . . . . . . . . . . . . equation for total hours
• 6a + 6.6b = 175.8 . . . . . . equation for total pay