Linda and Angela contract to paint a neighbor's house.

Hi M7MBA,

We're told that Linda and Angela contract to paint a neighbor's house and Linda spends 50% more time painting the house than Angela does. We're also told that each receives a payment of M dollars when the work is completed and Angela decides to pay Linda N dollars so that they would have received the SAME compensation per HOUR worked. We're asked for the value of N in terms of M. This question can be solved in a couple of different ways. Here's how you can TEST VALUES to get the answer.

IF....
Angela works 2 hours
Linda works 3 hours
M = $25, so the TOTAL paid is $50

$50 for 5 total hours of work is $50/5 = $10/hour. Thus, Angela would pay Linda $5 (so that Angela would have $20 for 2 hours of work and Linda would have $30 for 3 hours of work). Thus, N = $5 when M = $25

Final Answer: D

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M7MBA wrote:Linda and Angela contract to paint a neighbor's house. Even though Linda spends 50% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m

The OA is D .

I am really confuse here. I don't know how to solve it. Experts, I would love your help. Thanks in advance.

We can let t = the amount of time Angela worked and create the equation:

(m - n)/t = (m + n)/(1.5t)

1.5t(m - n) = t(m + n)

1.5(m - n) = (m + n)

1.5m - 1.5n = m + n

0.5m = 2.5n

5m = 25n

5m/25 = n

m/5 = n

(1/5)m = n

Alternate Solution:

Let’s assume that Angela worked 10 hours, and, thus, Linda worked 15 hours. After Angela gives n dollars to Linda, we see that Angela has (m - n) dollars, and Linda has (m + n) dollars. Since this exchange of dollars makes the hourly wage of each painter equal, we have:

Angela’s hourly wage = Linda’s hourly wage

(m - n)/10 = (m + n)/15

15m - 15n = 10m + 10n

5m = 25n

m/5 = n

(1/5)m = n

Answer: D