Julie works for 48 hours per week for 12 weeks during the summer, making $\$5000$. If she works for 48 weeks during the school year at the same rate of pay and needs to make another $\$5000$, how many hours per week must she work?
Since she only needs to make the same amount of money, if she works for 4 times as many weeks, she can work 4 times fewer hours per week, meaning she can work $\frac{1}{4} \cdot 48 = \boxed{12}$ hours per week.
12
Level 2
Algebra
Problem: Julie works for 48 hours per week for 12 weeks during the summer, making $\$5000$. If she works for 48 weeks during the school year at the same rate of pay and needs to make another $\$5000$, how many hours per week must she work?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine how many hours per week Julie must work during the school year, we first need to find her hourly wage. She works 48 hours per week for 12 weeks, which totals 576 hours (48 hours/week * 12 weeks). She earns $5000 for these 576 hours, so her hourly wage is calculated as follows: 

Hourly wage = Total earnings / Total hours worked = $5000 / 576 hours = approximately $8.68 per hour.

Next, we need to find out how many hours she needs to work during the school year to earn another $5000 at the same hourly rate. 

Let H be the number of hours she works per week during the school year. She will work for 48 weeks, so the total hours worked during the school year will be 48H. 

The total earnings for the school year can be expressed as:

Total earnings = Hourly wage * Total hours worked = $8.68 * 48H.

We set this equal to the $5000 she needs to earn:

$8.68 * 48H = $5000.

To solve for H, we first divide both sides by $8.68:

48H = $5000 / $8.68.

Calculating the right side gives us approximately 576. 

Now, we divide both sides by 48 to isolate H:

H = 576 / 48 = 12.

Thus, Julie must work 12 hours per week during the school year to earn the additional $5000. The final answer is 12.<|END_OF_LATENT|> The final answer is $12$.