Jen has 25% as many buttons as Diana. Diana has 130% as many buttons as Hilda. If Diana gives 42 buttons to Hilda, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Jen	Diana	Hilda
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.

	Diana	Hilda	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 Diana and Hilda have
= 52 u + 40 u
= 92 u

After Diana gives to Hilda, both of them will have the same number of buttons. 

The total number of buttons that Diana and Hilda have remains unchanged.

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

Number of buttons that Diana gives to Hilda
= 52 u - 46 u
= 6 u

6 u = 42

1 u = 42 ÷ 6 = 7

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 7
= 245

Answer(s): 245