Question

Charlie has a giant bag of gumballs and wants to share them with his friends. He gives half of what he has to his buddy, Jaysen. He gives half of what's left after that to Marinda. Then he gives half of what's left now to Zack. His mom makes him give 5 gumballs to his sister. Now he has 10 gumballs left. How many gumballs did Charlie have to begin with?

Answer 1

120 gumballs

Explanation:

Let

x = total gumballs

Buddy = 1/2x

Balance = x - 1/2x

= 2x-x/2

= 1/2x

Miranda = 1/2 of 1/2x

= 1/2 × 1/2x

= 1/4x

Balance = 1/2x - 1/4x

= 2x-x/4

= 1/4x

Zack = 1/2 of 1/4x

= 1/2 × 1/4x

= 1/8x

Balance = 1/4x - 1/8x

= 2x-x/8

= 1/8x

His sister = 5

Balance = 1/8x -5

10 = 1/8x - 5

10 + 5 = 1/8x

15 = 1/8x

x = 15 ÷ 1/8

= 15 × 8/1

= 120

x = 120 gumballs