Natalie and Jade have some cupcakes each. If Natalie gives Jade 19 cupcakes, Natalie will have ¹₈ as many cupcakes as Jade. If Natalie gives Jade 7 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Jade have at first?

	Case 1		Case 2
	Natalie	Jade	Natalie	Jade
Before	1 u + 19	8 u - 19	4.5 u + 7	4.5 u - 7
Change	- 19	+ 19	- 7	+ 7
After	1 u	8 u	4.5 u	4.5 u

Total number of cupcakes that Natalie and Jade have
= 1 u + 8 u
= 9 u 

Number of cupcakes that Natalie and Jade each has in the end is the same.

Number of cupcakes that Natalie and Jade each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u

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

4.5 u + 7 = 1 u + 19
4.5 u - 1 u = 19 - 7
0.5 u = 12

1 u = 12 ÷ 0.5 = 24

Number of cupcakes that Jade has
= 8 u - 19
= 8 x 24 - 19
= 192 - 19
= 173

Answer(s): 173