Ahmad had some chocolate chip cupcakes and cheese cupcakes. ³₅ of the number of chocolate chip cupcakes was equal to ¹₇ of the number of cheese cupcakes. After Ahmad made 27 more chocolate chip cupcakes, the number of chocolate chip cupcakes was ²₃ of the number of cheese cupcakes. How many cupcakes did he have altogether in the end?
Make the numerators the same. LCM of 3 and 1 is 3.

35 of chocolate chip cupcakes = 1x37x3 of cheese cupcakes

³₅ of chocolate chip cupcakes = ³₂₁ of cheese cupcakes

	Chocolate chip cupcakes	Cheese cupcakes	Total
Before	5 u	21 u
Change	+ 27
After	2x7 = 14 u	3x7 = 21 u	35 u

The number of cheese cupcakes remains unchanged.  Make the number of cheese cupcakes the same.  LCM of 3 and 21 is 21.

Number of more chocolate chip cupcakes made
= 14 u - 5 u
= 9 u

9 u = 27

1 u = 27 ÷ 9 = 3

Number of cupcakes that Ahmad had in the end
= 14 u + 21 u
= 35 u
= 35 x 3
= 105

Answer(s): 105