Esther and Marion collected buttons. Esther gave 30% of her buttons to Marion and as a result, Marion's buttons increased by 10%. If Esther had 84 buttons left, find the number of buttons Marion should give to Esther in the end so that both had an equal number of buttons.

	Esther	Marion	Comparing the change in Marion'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 Marion had is repeated.  Make the increase in the number of buttons that Marion had the same. LCM of 3 and 1 = 3

7 u = 84

1 u = 84 ÷ 7 = 12

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

Number of buttons that Marion should give to Esther so that both had an equal number of buttons in the end
= 26 u ÷ 2
= 13 u
= 13 x 12
= 156

Answer(s): 156