swerve wrote: ↑

Wed Sep 09, 2020 5:47 am

Sam's car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?

A. $13
B. $15
C. $20
D. $28
E. $48

The OA is C

Source: Magoosh

Let F = the total cost of the fine

Joe paid $3 more than 1/4 of the fine
So, F/4 + 3 = the amount Joe paid

Peter paid $3 less than 1/3 of the fine
So, F/3 - 3 = the amount Peter paid

Sam paid $4 less than 1/2 the fine
So, F/2 - 4 = the amount Sam paid

(amount Joe paid) + (amount Peter paid) + (amount Sam paid) = total cost of fine
We can write: (F/4 + 3) + (F/3 - 3 ) + (F/2 - 4) = F
To eliminate the fractions, we'll multiply both sides of the equation by 12 (the least common multiple of 3, 4 and 2)
When we do this, we get: 3F + 36 + 4F - 36 + 6F - 48 = 12F
Simplify to get: 13F - 48 = 12F
Solve: F = 48

What fraction of the fine did Sam pay?
F/2 - 4 = the amount Sam paid
So, 48/2 - 4 = the amount Sam paid
Evaluate to see that Sam paid $20

Answer: C

ASIDE: the question asks What fraction of the fine did Sam pay?
So, the answer SHOULD be 20/48

Cheers,
Brent