Vincent has 10% as many buttons as Paul. If Vincent gives away 50% of the buttons and Paul gives away 80% of his buttons, they will have 60 buttons altogether. How many buttons do the two of them have?

	Vincent	Paul	Total
Comparing Vincent and Paul at first	1x2 = 2 u	10x2 = 20 u
Before	2x1 = 2 u	5x4 =  20 u
Change	- 1x1 = - 1 u	- 4x4 = - 16 u
After	1x1 = 1 u	1x4 = 4 u	60

10% = ¹⁰₁₀₀ = ¹₁₀

50% = ⁵⁰₁₀₀ = ¹₂ 

80% =⁸⁰₁₀₀ = ⁴₅ 

The number of buttons that Vincent has at first is repeated.  Make the number of buttons that Vincent has the same.  LCM of 1 and 2 is 2 u.

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

Number of buttons in the end
= 1 u + 4 u
= 5 u

5 u = 60

1 u = 60 ÷ 5 = 12

Total number of buttons that the two of them have
= 2 u + 20 u
= 22 u
= 22 x 12
= 264

Answer(s): 264