Elijah has 70% as many buttons as Asher. If Elijah gives away 25% of the buttons and Asher gives away 20% of his buttons, they will have 583 buttons altogether. How many buttons do the two of them have?

	Elijah	Asher	Total
Comparing Elijah and Asher at first	7x4 = 28 u	10x4 = 40 u
Before	4x7 = 28 u	5x8 =  40 u
Change	- 1x7 = - 7 u	- 1x8 = - 8 u
After	3x7 = 21 u	4x8 = 32 u	583

70% = ⁷⁰₁₀₀ = ⁷₁₀

25% = ²⁵₁₀₀ = ¹₄ 

20% =²⁰₁₀₀ = ¹₅ 

The number of buttons that Elijah has at first is repeated.  Make the number of buttons that Elijah has the same.  LCM of 7 and 4 is 28 u.

The number of buttons that Asher has at first is repeated. Make the number of buttons that Asher has the same. LCM of 10 and 5 is 40 u.

Number of buttons in the end
= 21 u + 32 u
= 53 u

53 u = 583

1 u = 583 ÷ 53 = 11

Total number of buttons that the two of them have
= 28 u + 40 u
= 68 u
= 68 x 11
= 748

Answer(s): 748