Elyse made 275 more coffee shortbreads than cheese shortbreads. After she gave away ⁴₇ of the coffee shortbreads and ¹₈ of the cheese shortbreads, there were an equal number of coffee shortbreads and cheese shortbreads left. How many coffee shortbreads did she give away?

	Coffee shortbreads	Cheese shortbreads	Difference
Before	7x7 = 49 u	8x3 = 24 u	25 u
Change	- 4x7 = - 28 u	- 1x3 = - 3 u
After	3x7 = 21 u	7x3 = 21 u

Fraction of coffee shortbreads left
= 1 - ⁴₇
= ³₇

Fraction of cheese shortbreads left
= 1 - ¹₈
= ⁷₈

The number of coffee shortbreads and cheese shortbreads in the end is the same. Make the numerators the same.  LCM of 7 and 3 is 21.

³₇ of coffee shortbreads = ⁷₈ of cheese shortbreads
²¹₄₉ of coffee shortbreads = ²¹₂₄ of cheese shortbreads

Number of more coffee shortbreads than cheese shortbreads at first
= 49 u - 24 u
= 25 u

25 u = 275

1 u = 275 ÷ 25 = 11

Number of coffee shortbreads that Elyse gave away
= 49 u - 21 u
= 28 u
= 28 x 11
= 308

Answer(s): 308