Fiona and Rachel collected buttons. Fiona gave 30% of her buttons to Rachel and as a result, Rachel's buttons increased by 10%. If Fiona had 35 buttons left, find the number of buttons Rachel should give to Fiona in the end so that both had an equal number of buttons.

	Fiona	Rachel	Comparing the change in Rachel's buttons
Before	10x1 = 10 u		10x3 = 30u
Change	- 3x1 = - 3 u	+ 3x1 = + 3 u	+ 1x3 = + 3 u
After	7x1 = 7 u		11x3 = 33 u

30% = ³⁰₁₀₀ = ³₁₀
10% = ¹⁰₁₀₀ = ¹₁₀

The increase in the number of buttons that Rachel had is repeated.  Make the increase in the number of buttons that Rachel had the same. LCM of 3 and 1 = 3

7 u = 35

1 u = 35 ÷ 7 = 5

Number of buttons that Rachel had more than Fiona in the end
= 33 u - 7 u
= 26 u

Number of buttons that Rachel should give to Fiona so that both had an equal number of buttons in the end
= 26 u ÷ 2
= 13 u
= 13 x 5
= 65

Answer(s): 65