Problem Solving

BTGmoderatorLU wrote: ↑

Fri Nov 13, 2020 4:37 am

Source: Magoosh

After taxes, Sally takes home a salary of J=$5000 every month. She pays P percent of this to her rent and all her fixed bills each month, leaving her with K left. She spends half of K on groceries, leaving her with L left. If she spends \(\dfrac{1}{3}\) of L on gifts and puts \(\dfrac{2}{5}\) of L into her savings account, this would leave her with $200 for miscellaneous expenses. What is the value of P?

A. 30
B. 40
C. 50
D. 60
E. 70

The OA is E

Solution:

We see that K = 5000 - 5000 x P/100 = 5000 - 50P and therefore, L = 1/2 x (5000 - 50P) = 2500 - 25P. Finally, we can create the equation:

L - 1/3 x L - 2/5 x L = 200

15/15 x L - 5/15 x L - 6/15 x L = 200

4/15 x L = 200

4L = 3000

4(2500 - 25P) = 3000

10000 - 100P = 3000

7000 = 100P

70 = P

Alternate Solution:

We will work backwards and first determine the value of L. Notice that after L/3 was spent on gifts and 2L/5 was saved, the amount of money left for Sally in terms of L was L - (L/3 + 2L/5) = L - 11L/15 = 4L/15. We are told that this is equal to $200, thus:

4L/15 = 200

L = (200 * 15)/4 = 750

Next, we know that L is half of K. Since L = $750, it follows that K = $1,500.

Finally, we are told that after the rent and expenses were paid, Sally had K = $1,500 remaining. This means that the rent and expenses cost 5,000 - 1,500 = $3,500. Since $3,500 is P percent of $5,000, we have:

5,000 * P/100 = 3,500

P = (3,500 * 100)/5,000 = 70

Answer: E