A Little Tricky Algebra Word Problem

Navin spent 25% of it and gave 2/5 of the remainder to his brother. He then spent the remainder amount on 9 story books. If each story book costs 12, how much did he have at first.

Solution

Let x be the amount that Navin had at first.

If Navin spend 25% of x, then he is left with 75% of x, 0.75x or (3/4)x.


Next, Navin gave 2/5 of the remainder to his brother.

2/5 of 0.75x = 2/5 × (3/4)x = (6/20)x = (3/10)x

He is left with (3/4)x - (3/10)x.

(3/4)x - (3/10)x = (30/40)x - (12/40)x = (18/40)x = (9/20)x

Navin spent 9 × 12 or 108 dollars on story books.


Navin is going to spend all the money that is left or (9/20)x on story books costing 108 dollars.

Therefore, (9/20)x = 108

Multiply both sides by 20/9

(20/9)(9/20)x = 108(20/9)

x = 2160/9

x = 240 dollars.

Navin started with 240 dollars.