Rachel made 161 more mocca scones than cream scones. After she gave away ⁵₇ of the mocca scones and ¹₆ of the cream scones, there were an equal number of mocca scones and cream scones left. How many mocca scones did she give away?

	Mocca scones	Cream scones	Difference
Before	7x5 = 35 u	6x2 = 12 u	23 u
Change	- 5x5 = - 25 u	- 1x2 = - 2 u
After	2x5 = 10 u	5x2 = 10 u

Fraction of mocca scones left
= 1 - ⁵₇
= ²₇

Fraction of cream scones left
= 1 - ¹₆
= ⁵₆

The number of mocca scones and cream scones in the end is the same. Make the numerators the same.  LCM of 5 and 2 is 10.

²₇ of mocca scones = ⁵₆ of cream scones
¹⁰₃₅ of mocca scones = ¹⁰₁₂ of cream scones

Number of more mocca scones than cream scones at first
= 35 u - 12 u
= 23 u

23 u = 161

1 u = 161 ÷ 23 = 7

Number of mocca scones that Rachel gave away
= 35 u - 10 u
= 25 u
= 25 x 7
= 175

Answer(s): 175