David had some cherry shortbreads and chocolate chip shortbreads. ²₅ of the number of cherry shortbreads was equal to ¹₈ of the number of chocolate chip shortbreads. After David made 152 more cherry shortbreads, the number of cherry shortbreads was ³₂ of the number of chocolate chip shortbreads. How many shortbreads did he have altogether in the end?
Make the numerators the same. LCM of 2 and 1 is 2.

25 of cherry shortbreads = 1x28x2 of chocolate chip shortbreads

²₅ of cherry shortbreads = ²₁₆ of chocolate chip shortbreads

	Cherry shortbreads	Chocolate chip shortbreads	Total
Before	5 u	16 u
Change	+ 152
After	3x8 = 24 u	2x8 = 16 u	40 u

The number of chocolate chip shortbreads remains unchanged.  Make the number of chocolate chip shortbreads the same.  LCM of 2 and 16 is 16.

Number of more cherry shortbreads made
= 24 u - 5 u
= 19 u

19 u = 152

1 u = 152 ÷ 19 = 8

Number of shortbreads that David had in the end
= 24 u + 16 u
= 40 u
= 40 x 8
= 320

Answer(s): 320