Math Word Problem

Question

Brendan spent 3/4 of his money on a three piece suite. He spent 1/2 of the remainder on a new book. The suit cost $30 more than the book. how much did the book cost?

Answer 1

1 - 3/4 = 1/4 <--- what remains after buying the 3 piece suit

Half of that is 1/4*1/2 = 1/8 , so 1/8 is the fraction of the money spent on the book

Suppose he has N dollars, $N at the beginning.

The suits costs (3/4)N

the book costs (1/8)N

(3/4)N = (1/8)N + 30 <--- the suit costs $30 more than the book

6N = N + 240 <--- multiplies everything by 8 to clear the fractions

5N = 240

N = 240/5 = 48

He starts with $48

3/4 of $48 is $36 is the price of the 3 piece suit

1/8 of $48 is $6 is the price of the book

He has $6 left.

Note that the 3 piece suit is $30 more than the book

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