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.
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.
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