Barbara and Sabrina have some cupcakes each. If Barbara gives Sabrina 32 cupcakes, Barbara will have ⁷₈ as many cupcakes as Sabrina. If Barbara gives Sabrina 9 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Sabrina have at first?

	Case 1		Case 2
	Barbara	Sabrina	Barbara	Sabrina
Before	7 u + 32	8 u - 32	7.5 u + 9	7.5 u - 9
Change	- 32	+ 32	- 9	+ 9
After	7 u	8 u	7.5 u	7.5 u

Total number of cupcakes that Barbara and Sabrina have
= 7 u + 8 u
= 15 u 

Number of cupcakes that Barbara and Sabrina each has in the end is the same.

Number of cupcakes that Barbara and Sabrina each has in the end in Case 2
= 15 u ÷ 2
= 7.5 u

Number of cupcakes that Barbara had at first is the same in Case 1 and Case 2.

7.5 u + 9 = 7 u + 32
7.5 u - 7 u = 32 - 9
0.5 u = 23

1 u = 23 ÷ 0.5 = 46

Number of cupcakes that Sabrina has
= 8 u - 32
= 8 x 46 - 32
= 368 - 32
= 336

Answer(s): 336