Mason had 25% more buttons than Isaiah. Harper had 50% fewer buttons than Mason. Mason and Isaiah gave Harper some buttons in the ratio of 3 : 4. As a result, Harper had 60% more buttons than before. Given that Isaiah had 132 less buttons than Harper in the end, how many buttons did Isaiah give to Harper?

Mason	Isaiah	Harper
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Mason : Isaiah = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Mason : Harper = 2 : 1

The number of buttons that Mason had at first is repeated. Make the number of buttons that Mason had at first the same.  LCM of 5 and 2 is 10.

	Mason	Isaiah	Harper
Before	10x7 =  70 u	8x7 = 56 u	5x7 = 35 u
Change			+ 3x7 = + 21 u
Comparing the changes in the number of buttons	- 3x3 = - 9 u	- 4x3 = - 12 u	+ 7x3 = + 21 u
After	61 u	44 u	8x7 = 56 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of buttons that Mason and Isaiah gave to Harper is repeated.  Make the total number of buttons that Mason and Isaiah gave to Harper the same.  LCM of 7 and 3 is 21.

Number of buttons that Isaiah had less than Harper 
= 56 u - 44 u
= 12 u

12 u = 132

1 u = 132 ÷ 12 = 11

Number of buttons that Isaiah gave to Harper
= 12 u
= 12 x 11
= 132

Answer(s): 132