Zara made 10 more cheese biscuits than coffee biscuits. After she gave away ⁴₇ of the cheese biscuits and ¹₃ of the coffee biscuits, there were an equal number of cheese biscuits and coffee biscuits left. How many cheese biscuits did she give away?

	Cheese biscuits	Coffee biscuits	Difference
Before	7x2 = 14 u	3x3 = 9 u	5 u
Change	- 4x2 = - 8 u	- 1x3 = - 3 u
After	3x2 = 6 u	2x3 = 6 u

Fraction of cheese biscuits left
= 1 - ⁴₇
= ³₇

Fraction of coffee biscuits left
= 1 - ¹₃
= ²₃

The number of cheese biscuits and coffee biscuits in the end is the same. Make the numerators the same.  LCM of 2 and 3 is 6.

³₇ of cheese biscuits = ²₃ of coffee biscuits
⁶₁₄ of cheese biscuits = ⁶₉ of coffee biscuits

Number of more cheese biscuits than coffee biscuits at first
= 14 u - 9 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

Number of cheese biscuits that Zara gave away
= 14 u - 6 u
= 8 u
= 8 x 2
= 16

Answer(s): 16