Gareth and Mahesh

Algebra Level 2

Gareth and Mahesh had an equal amount of money in their Piggy Bank. When Gareth spent $ 24 \$24 and Mahesh spent $ 72 \$72 , Gareth had 3 3 times as much money as Mahesh.

How much money did each of them have at first?

$48 $96 $69 $92

Ethan Mandelez by Ethan Mandelez , 15, Malaysia

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3 solutions

Chew-Seong Cheong
Nov 26, 2020

Let Gareth and Mahesh originally had $ x \$x . Then we have

x − 24 = 3 ( x − 72 ) x − 24 = 3 x − 216 3 x − x = 216 − 24 2 x = 192 ⟹ x = 96 \begin{aligned} x-24 & = 3(x-72) \\ x - 24 & = 3x - 216 \\ 3x - x & = 216 - 24 \\ 2x & = 192 \\ \implies x & = 96 \end{aligned}

Therefore each of them originally had $ 96 \boxed{\$96} .

2 Helpful 1 Interesting 1 Brilliant 0 Confused
Rhea Kavuru
Nov 27, 2020

If x x is the amount of money they had at first, then....

x − 24 = 3 ( x − 72 ) x-24 = 3(x-72)

x − 24 = 3 x − 216 x-24 = 3x-216

− 2 x = − 192 -2x = -192

x = 96 x = 96

1 Helpful 1 Interesting 1 Brilliant 0 Confused
Ethan Mandelez
Nov 26, 2020

This problem is pretty straightforward, here's my approach:

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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