Respuesta :
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
[tex]x-\dfrac{1}{3}x=\dfrac{2}{3}x[/tex]
He uses the remaining 2/5 to buy a video game. Then the remaining amount is
[tex]Remaining=\dfrac{2}{3}x-\dfrac{2}{3}x\times \dfrac{2}{5}[/tex]
[tex]Remaining=\dfrac{2}{3}x-\dfrac{4}{15}x[/tex]
[tex]Remaining=\dfrac{10x-4x}{15}[/tex]
[tex]Remaining=\dfrac{6x}{15}[/tex]
[tex]Remaining=\dfrac{2x}{5}[/tex]
It is given that the remaining amount is $12.
[tex]12=\dfrac{2x}{5}[/tex]
[tex]12\times 5=2x[/tex]
[tex]60=2x[/tex]
Divide both sides by 2.
[tex]\dfrac{60}{2}=x[/tex]
[tex]30=x[/tex]
Therefore, Bobby have $30 at first.
