Question

In one week Jenny worked a total of 22 hours at a movie theater and a car wash. She earned $8.50 per hour at the movie and $8.00 per hour at the car wash. She earned a total of $181 for the week. How many hours did Jenny work at the car wash?

a) 8
b) 10
c) 11
d) 12

Answer 1

Using a system of equations where x represents the hours at the movie theater and y the hours at the car wash, we determined that Jenny worked 12 hours at the car wash. The correct answer is (d) 12.

Step-by-step explanation:

To determine how many hours Jenny worked at the car wash, we can set up a system of equations based on the information given. Let x be the number of hours Jenny worked at the movie theater and y be the number of hours she worked at the car wash. The total hours worked in the week is given as 22, so we can write our first equation as x + y = 22.

The total earnings can be represented by the equation 8.50x + 8.00y = 181 because she earns $8.50 per hour at the movie theater and $8.00 per hour at the car wash. Now we have a system of equations:

1. x + y = 22
2. 8.50x + 8.00y = 181

Solving the first equation for x in terms of y (x = 22 - y) and substituting into the second equation gives us:

8.50(22 - y) + 8.00y = 181

Expanding and simplifying this equation:

187 - 8.50y + 8.00y = 181

Combining like terms:

-0.50y = -6

Dividing by -0.50:

y = 12

So Jenny worked 12 hours at the car wash. The correct answer is (d) 12.