Bobby had some apple shortbreads and strawberry shortbreads. ²₃ of the number of apple shortbreads was equal to ¹₈ of the number of strawberry shortbreads. After Bobby made 30 more apple shortbreads, the number of apple shortbreads was ¹₂ of the number of strawberry shortbreads. How many shortbreads did he have altogether in the end?
Make the numerators the same. LCM of 2 and 1 is 2.

23 of apple shortbreads = 1x28x2 of strawberry shortbreads

²₃ of apple shortbreads = ²₁₆ of strawberry shortbreads

	Apple shortbreads	Strawberry shortbreads	Total
Before	3 u	16 u
Change	+ 30
After	1x8 = 8 u	2x8 = 16 u	24 u

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

Number of more apple shortbreads made
= 8 u - 3 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

Number of shortbreads that Bobby had in the end
= 8 u + 16 u
= 24 u
= 24 x 6
= 144

Answer(s): 144