Jen has 25% as many buttons as Betty. Betty has 130% as many buttons as Emma. If Betty gives 12 buttons to Emma, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Jen	Betty	Emma
1x13	4x13
	13x4	10x4
13 u	52 u	40 u

25% = ²⁵₁₀₀ = ¹₄
130% = ¹³⁰₁₀₀= ¹³₁₀

The number of buttons that Jen has is repeated.  Make the number of buttons that Jen has the same. LCM of 4 and 13 is 52.

	Betty	Emma	Total
Before	52 u	40 u	92 u
Change	- 6 u	+ 6 u
After	46 u	46 u	92 u

Total number of buttons that Betty and Emma have
= 52 u + 40 u
= 92 u

After Betty gives to Emma, both of them will have the same number of buttons. 

The total number of buttons that Betty and Emma have remains unchanged.

Number of buttons that each of them will have
= 92 u ÷ 2
= 46 u

Number of buttons that Betty gives to Emma
= 52 u - 46 u
= 6 u

6 u = 12

1 u = 12 ÷ 6 = 2

Total number of buttons that three of them have
= 92 u + 13 u
= 105 u

Average number of buttons that each of them have
= 105 u ÷ 3
= 35 u
= 35 x 2
= 70

Answer(s): 70