Question

Kara earned $136.75 last week, working 16 hours. She earned $10.50 per hour at the fast food restaurant and $4.25 per hour helping her aunt clean her store.

How many hours did she work at the fast food restaurant? How many hours did she help her aunt clean the store? In your response, make sure to:

Create a model that can be used to determine the number of hours Kara worked at each job.
Define your variables.
Show all work.

Answer 1

Answer: Aunt for 5 hours and Fast Food for 11 hpurs

Explanation:

Let F be the hours worked at the fast Food restaurant and A the hours worked for her Aunt.

We know that:

F($10.50/hr) + A($4.25/hr) = $136.75

We also know that F + A = 16 hours

Rearrange the second equation to solve for one of the variable. I'll pick F.

F = 16 - A

Use this in the first equation:

F($10.50/hr) + A($4.25/hr) = $136.75

(16-A)(10.50) + A(4.25) = 136.75

168 - 10.5A + 4.25A = 136.75

- 6.25A = -31.24

A = 4.9984 or 5 hours

That means she worked at the fast food restaurant for (16-5) = 11 hours

(5 hr)*($4.25/hr) + (11 hr)*($10.50/hr) =

$21.25 + $115.5 = $136.75