Working her way through school, Liz works two part-time jobs for a total of 28 hours a week. Job A pays $5.80 per hour, and Job B pays $7.20 per hour. How many hours did she work at each job the week that she made $184.80?

Liz worked 12 hours at Job A, which pays $5.80 per hour, and 16 hours at Job B, which pays $7.20 per hour. We calculated this by setting up a system of equations based on the total hours worked and the total amount earned, and then solving for each variable.

Explanation:

To find out how many hours Liz worked at each job, we need to set up a system of equations with two variables.

Let's call the number of hours she worked at Job A x and the number of hours at Job B y. We are given that she works a total of 28 hours a week and that she made $184.80 in that week. We can set up the following equations:

Equation for total hours: x + y = 28
Equation for total earnings: 5.80x + 7.20y = 184.80

Now, we will solve this system of equations using the substitution or elimination method. Let's use the substitution method here:

Solve the first equation for x: x = 28 - y.
Substitute x in the second equation: 5.80(28 - y) + 7.20y = 184.80.
Simplify and solve for y: 162.40 - 5.80y + 7.20y = 184.80, which simplifies to 1.40y = 22.40 and then y = 16.
Substitute y back into x = 28 - y to find x: x = 28 - 16, so x = 12.

Therefore, Liz worked 12 hours at Job A and 16 hours at Job B.

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