Question

Bobby put 1/3 of his lawn mowing money into his savings and uses the remaining 2/5 to buy a video game. If he has $12 left, how much did he have at first?

Answer 1

Given:

Bobby put 1/3 of his lawn mowing money into his savings

He uses the remaining 2/5 to buy a video game.

He has $12 left.

To find:

The amount did he have at first.

Solution:

Let x be the initial amount.

Bobby put 1/3 of his lawn mowing money into his savings. So, the remaining amount is

$x-\dfrac{1}{3}x=\dfrac{2}{3}x$

He uses the remaining 2/5 to buy a video game. Then the remaining amount is

$Remaining=\dfrac{2}{3}x-\dfrac{2}{3}x\times \dfrac{2}{5}$

$Remaining=\dfrac{2}{3}x-\dfrac{4}{15}x$

$Remaining=\dfrac{10x-4x}{15}$

$Remaining=\dfrac{6x}{15}$

$Remaining=\dfrac{2x}{5}$

It is given that the remaining amount is $12.

$12=\dfrac{2x}{5}$

$12\times 5=2x$

$60=2x$

Divide both sides by 2.

$\dfrac{60}{2}=x$

$30=x$

Therefore, Bobby have $30 at first.