Michael had some chocolate chip cupcakes and blueberry cupcakes. ²₅ of the number of chocolate chip cupcakes was equal to ¹₈ of the number of blueberry cupcakes. After Michael made 209 more chocolate chip cupcakes, the number of chocolate chip cupcakes was ³₂ of the number of blueberry cupcakes. How many cupcakes did he have altogether in the end?
Make the numerators the same. LCM of 2 and 1 is 2.

25 of chocolate chip cupcakes = 1x28x2 of blueberry cupcakes

²₅ of chocolate chip cupcakes = ²₁₆ of blueberry cupcakes

	Chocolate chip cupcakes	Blueberry cupcakes	Total
Before	5 u	16 u
Change	+ 209
After	3x8 = 24 u	2x8 = 16 u	40 u

The number of blueberry cupcakes remains unchanged.  Make the number of blueberry cupcakes the same.  LCM of 2 and 16 is 16.

Number of more chocolate chip cupcakes made
= 24 u - 5 u
= 19 u

19 u = 209

1 u = 209 ÷ 19 = 11

Number of cupcakes that Michael had in the end
= 24 u + 16 u
= 40 u
= 40 x 11
= 440

Answer(s): 440