Bert left the house with \(N\) dollars. He spent 1/4 of this

M7MBA wrote:Bert left the house with \(N\) dollars. He spent 1/4 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $10 left in his pocket. What was the value of \(N?\)

A. $36
B. $44
C. $52
D. $60
E. $68

[spoiler]OA=A[/spoiler]

Source: Magoosh

Since Bert spends 1/4 of his money at the hardware store, he has 3N/4 left.

Since he spends 7 dollars at the dry cleaners, he has 3N/4 - 7 left.

We are given that he spends half of his remaining money at the grocery store, and after that, he has 10 dollars left. Thus, half of 3N/4 - 7 must equal 10; in other words:

1/2(3N/4 - 7) = 10

3N/4 - 7 = 20

3N/4 = 27

N/4 = 9

N = 36.

Alternate Solution:

Since Bert had $10 when he got home, he must have $20 before he spent half his money at the grocery store. Then, before the dry cleaners, he had 20 + 7 = $27. This represents the amount of money he had after he spent 1/4 of his money at the hardware store; thus 3/4 of his money is equal to $27. Then, N must equal 27/(3/4) = $36.

Answer: A