Jen has 25% as many buttons as Elyse. Elyse has 130% as many buttons as Hazel. If Elyse gives 60 buttons to Hazel, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Jen	Elyse	Hazel
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.

	Elyse	Hazel	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 Elyse and Hazel have
= 52 u + 40 u
= 92 u

After Elyse gives to Hazel, both of them will have the same number of buttons. 

The total number of buttons that Elyse and Hazel have remains unchanged.

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

Number of buttons that Elyse gives to Hazel
= 52 u - 46 u
= 6 u

6 u = 60

1 u = 60 ÷ 6 = 10

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 10
= 350

Answer(s): 350