Pamela has 25% as many buttons as Penelope. Penelope has 130% as many buttons as Zara. If Penelope gives 18 buttons to Zara, both will then have an equal number of buttons. Find the average number of buttons the three of them have.

Pamela	Penelope	Zara
1x13	4x13
	13x4	10x4
13 u	52 u	40 u

25% = ²⁵₁₀₀ = ¹₄
130% = ¹³⁰₁₀₀= ¹³₁₀

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

	Penelope	Zara	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 Penelope and Zara have
= 52 u + 40 u
= 92 u

After Penelope gives to Zara, both of them will have the same number of buttons. 

The total number of buttons that Penelope and Zara have remains unchanged.

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

Number of buttons that Penelope gives to Zara
= 52 u - 46 u
= 6 u

6 u = 18

1 u = 18 ÷ 6 = 3

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 3
= 105

Answer(s): 105