Barbara made 363 more blueberry biscuits than apple biscuits. After she gave away ⁵₇ of the blueberry biscuits and ¹₈ of the apple biscuits, there were an equal number of blueberry biscuits and apple biscuits left. How many blueberry biscuits did she give away?

	Blueberry biscuits	Apple biscuits	Difference
Before	7x7 = 49 u	8x2 = 16 u	33 u
Change	- 5x7 = - 35 u	- 1x2 = - 2 u
After	2x7 = 14 u	7x2 = 14 u

Fraction of blueberry biscuits left
= 1 - ⁵₇
= ²₇

Fraction of apple biscuits left
= 1 - ¹₈
= ⁷₈

The number of blueberry biscuits and apple biscuits in the end is the same. Make the numerators the same.  LCM of 7 and 2 is 14.

²₇ of blueberry biscuits = ⁷₈ of apple biscuits
¹⁴₄₉ of blueberry biscuits = ¹⁴₁₆ of apple biscuits

Number of more blueberry biscuits than apple biscuits at first
= 49 u - 16 u
= 33 u

33 u = 363

1 u = 363 ÷ 33 = 11

Number of blueberry biscuits that Barbara gave away
= 49 u - 14 u
= 35 u
= 35 x 11
= 385

Answer(s): 385