Fanny and Betty collected buttons. Fanny gave 50% of her buttons to Betty and as a result, Betty's buttons increased by 30%. If Fanny had 33 buttons left, find the number of buttons Betty should give to Fanny in the end so that both had an equal number of buttons.

	Fanny	Betty	Comparing the change in Betty's buttons
Before	2x3 = 6 u		10x1 = 10u
Change	- 1x3 = - 3 u	+ 1x3 = + 3 u	+ 3x1 = + 3 u
After	1x3 = 3 u		13x1 = 13 u

50% = ⁵⁰₁₀₀ = ¹₂
30% = ³⁰₁₀₀ = ³₁₀

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

3 u = 33

1 u = 33 ÷ 3 = 11

Number of buttons that Betty had more than Fanny in the end
= 13 u - 3 u
= 10 u

Number of buttons that Betty should give to Fanny so that both had an equal number of buttons in the end
= 10 u ÷ 2
= 5 u
= 5 x 11
= 55

Answer(s): 55