Xavier had some cheese shortbreads and cherry shortbreads. ⁵₇ of the number of cheese shortbreads was equal to ¹₅ of the number of cherry shortbreads. After Xavier made 36 more cheese shortbreads, the number of cheese shortbreads was ²₅ of the number of cherry shortbreads. How many shortbreads did he have altogether in the end?
Make the numerators the same. LCM of 5 and 1 is 5.

57 of cheese shortbreads = 1x55x5 of cherry shortbreads

⁵₇ of cheese shortbreads = ⁵₂₅ of cherry shortbreads

	Cheese shortbreads	Cherry shortbreads	Total
Before	7 u	25 u
Change	+ 36
After	2x5 = 10 u	5x5 = 25 u	35 u

The number of cherry shortbreads remains unchanged.  Make the number of cherry shortbreads the same.  LCM of 5 and 25 is 25.

Number of more cheese shortbreads made
= 10 u - 7 u
= 3 u

3 u = 36

1 u = 36 ÷ 3 = 12

Number of shortbreads that Xavier had in the end
= 10 u + 25 u
= 35 u
= 35 x 12
= 420

Answer(s): 420