Nora has 25% as many buttons as Mary. Mary has 130% as many buttons as Gem. If Mary gives 48 buttons to Gem, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Nora	Mary	Gem
1x13	4x13
	13x4	10x4
13 u	52 u	40 u

25% = ²⁵₁₀₀ = ¹₄
130% = ¹³⁰₁₀₀= ¹³₁₀

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

	Mary	Gem	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 Mary and Gem have
= 52 u + 40 u
= 92 u

After Mary gives to Gem, both of them will have the same number of buttons. 

The total number of buttons that Mary and Gem have remains unchanged.

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

Number of buttons that Mary gives to Gem
= 52 u - 46 u
= 6 u

6 u = 48

1 u = 48 ÷ 6 = 8

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 8
= 280

Answer(s): 280