Carl, Tim and Will bought some cupcakes. After Carl ate ³₈ of his cupcakes, Tim ate ²₃ of his cupcakes and Will ate 6 cupcakes, each of them had the same number of cupcakes left. Carl had 21 less cupcakes than Tim at first.

1. How many cupcakes did Carl have at first?
2. How many cupcakes did the 3 of them buy altogether? 

	Carl	Tim	Will
Before	8 u	3x5 = 15 u	5 u + 6
Change	- 3 u	- 2x5 = - 10 u	- 6
After	5 u	1x5 = 5 u	5 u

(a)
The number of cupcakes that Carl and Tim each had in the end is the same. Make the number of cupcakes that Carl and Tim each had in the end the same.  LCM of 5 and 1 is 5.

Number of cupcakes that Carl had less than Tim at first
= 15 u - 8 u
= 7 u

7 u = 21

1 u = 21 ÷ 7 = 3

Number of cupcakes that Carl had at first
= 8 u
= 8 x 3
= 24 

(b)
Total number of cupcakes that the 3 of them bought
= 8 u + 15 u + 5 u + 6
= 28 u + 6
= 28 x 3 + 6
= 84 + 6
= 90

Answer(s): (a) 24; (b) 90