Jeremiah had 40% more buttons than Avery. Kaylee had 20% fewer buttons than Jeremiah. Jeremiah and Avery gave Kaylee some buttons in the ratio of 3 : 4. As a result, Kaylee had 50% more buttons than before. Given that Avery had 100 less buttons than Kaylee in the end, how many buttons did Avery give to Kaylee?

Jeremiah	Avery	Kaylee
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Jeremiah : Avery = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Jeremiah : Kaylee = 5 : 4

The number of buttons that Jeremiah had at first is repeated. Make the number of buttons that Jeremiah had at first the same.  LCM of 7 and 5 is 35.

	Jeremiah	Avery	Kaylee
Before	35x1 =  35 u	25x1 = 25 u	28x1 = 28 u
Change			+ 14x1 = + 14 u
Comparing the changes in the number of buttons	- 3x2 = - 6 u	- 4x2 = - 8 u	+ 7x2 = + 14 u
After	29 u	17 u	42x1 = 42 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of buttons that Jeremiah and Avery gave to Kaylee is repeated.  Make the total number of buttons that Jeremiah and Avery gave to Kaylee the same.  LCM of 7 and 14 is 14.

Number of buttons that Avery had less than Kaylee 
= 42 u - 17 u
= 25 u

25 u = 100

1 u = 100 ÷ 25 = 4

Number of buttons that Avery gave to Kaylee
= 8 u
= 8 x 4
= 32

Answer(s): 32