Zeph has 90% as many buttons as Jenson. If Zeph gives away 50% of the buttons and Jenson gives away 20% of his buttons, they will have 175 buttons altogether. How many buttons do the two of them have?

	Zeph	Jenson	Total
Comparing Zeph and Jenson at first	9x2 = 18 u	10x2 = 20 u
Before	2x9 = 18 u	5x4 =  20 u
Change	- 1x9 = - 9 u	- 1x4 = - 4 u
After	1x9 = 9 u	4x4 = 16 u	175

90% = ⁹⁰₁₀₀ = ⁹₁₀

50% = ⁵⁰₁₀₀ = ¹₂ 

20% =²⁰₁₀₀ = ¹₅ 

The number of buttons that Zeph has at first is repeated.  Make the number of buttons that Zeph has the same.  LCM of 9 and 2 is 18 u.

The number of buttons that Jenson has at first is repeated. Make the number of buttons that Jenson has the same. LCM of 10 and 5 is 20 u.

Number of buttons in the end
= 9 u + 16 u
= 25 u

25 u = 175

1 u = 175 ÷ 25 = 7

Total number of buttons that the two of them have
= 18 u + 20 u
= 38 u
= 38 x 7
= 266

Answer(s): 266