Reggie had some cranberry cupcakes and strawberry cupcakes. ³₅ of the number of cranberry cupcakes was equal to ¹₃ of the number of strawberry cupcakes. After Reggie made 10 more cranberry cupcakes, the number of cranberry cupcakes was ²₃ of the number of strawberry 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 cranberry cupcakes = 1x33x3 of strawberry cupcakes

³₅ of cranberry cupcakes = ³₉ of strawberry cupcakes

	Cranberry cupcakes	Strawberry cupcakes	Total
Before	5 u	9 u
Change	+ 10
After	2x3 = 6 u	3x3 = 9 u	15 u

The number of strawberry cupcakes remains unchanged.  Make the number of strawberry cupcakes the same.  LCM of 3 and 9 is 9.

Number of more cranberry cupcakes made
= 6 u - 5 u
= 1 u

1 u = 10

1 u = 10 ÷ 1 = 10

Number of cupcakes that Reggie had in the end
= 6 u + 9 u
= 15 u
= 15 x 10
= 150

Answer(s): 150