4th edition, guide 3, Linda and Angela contract to paint

[chuperman601]

4th Edition
Guide 3
Equations, Inequalities, and VICS
Question 10
Page 196

I am trying to solve the below question algebraically rather than through the hybrid method as mentioned in the book or through plugging in numbers.

Linda and Angela contract to paint neighbor's house. Even though Linda spends 50% more time painting the house then Angela, each receives the 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

My progress so far:

Let L = Linda's hours worked
Let A = Angela's hours worked
Let C = Total Paid to Angela and Linda

L = 1.5A since "Linda spends 50% more time painting the house then Angela"

C1 = (1.5A)/M + (A)/M since "each receives the payment of M dollars when the work is completed"

C2 = (1.5NA) + (NA)

Since the total amount would still be the same regardless of the method of payment, I went as follows:

C1 = C2 so....
(1.5A)/M + (A)/M = (1.5NA) + (NA)

Solving for N, I got N=(1/M)

Where did I go wrong?

Thank you

[rahul_var25]

I think u did mistake in calculating hourly wages b'coz question asks for compensation per hour .

since L = 1.5A time spent and both receives M dollars

and for equalising the hourly compensation Angela gave N dollars to Linda.

It means their wages become for
Linda = M+N (Receives)
Angela = M-N (Gave)

and

We must divide their individual wages by their respective work time to get their hourly compensation

For Linda = M+N/1.5
Angela = M-N/1

since their hourly wages are equal then,

M+N/1.5 = M-N/1 or by cross multiplying

M+N = 1.5M-1.5N
2.5N = 0.5M
N= (0.5/2.5)M = (5/25)M = (1/5)M

[chuperman601]

Thank you!

[jnelson0612]

Rahul, thank you and nice work!

This is a perfect example of why plugging numbers or using the hybrid makes huge sense over algebra on many problems. There is just too much room for error using algebra.