(a) How much money did Nestor spend on the books? Nestor spent $90 of his money on some toys in May. He spent 1/4 of the remaining money on some books. Then he had 1/3 of his money left.
Answer (1)
To find out how much money Nestor spent on books, let's break down the problem step-by-step.
First, define the initial amount of money Nestor had as x .
Nestor spent $90 on toys. So, the remaining amount was: x − 90
Nestor spent 4 1 of the remaining money on books. So, the amount he spent on books is: 4 1 ( x − 90 )
After buying the books, he was left with 3 1 of his initial money. Therefore: x − 90 − 4 1 ( x − 90 ) = 3 1 x
Now solve the equation:
Simplify and solve for x :
x − 90 − 4 1 ( x − 90 ) = 3 1 x
Multiply the entire equation by 12 to eliminate the fractions:
12 ( x − 90 ) − 3 ( x − 90 ) = 4 x
Simplifying:
9 x − 1080 = 4 x
Rearrange to get:
9 x − 4 x = 1080
5 x = 1080
Solve for x :
x = 5 1080
x = 216
Now, we know that Nestor initially had $216.
Calculate the amount spent on books:
4 1 ( 216 − 90 ) = 4 1 × 126
= 31.50
So, Nestor spent $31.50 on the books.
