Paul, Brandon and Gabriel bought some cupcakes. After Paul ate ⁵₈ of his cupcakes, Brandon ate ³₄ of his cupcakes and Gabriel ate 6 cupcakes, each of them had the same number of cupcakes left. Paul had 32 less cupcakes than Brandon at first.

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

	Paul	Brandon	Gabriel
Before	8 u	4x3 = 12 u	3 u + 6
Change	- 5 u	- 3x3 = - 9 u	- 6
After	3 u	1x3 = 3 u	3 u

(a)
The number of cupcakes that Paul and Brandon each had in the end is the same. Make the number of cupcakes that Paul and Brandon each had in the end the same.  LCM of 3 and 1 is 3.

Number of cupcakes that Paul had less than Brandon at first
= 12 u - 8 u
= 4 u

4 u = 32

1 u = 32 ÷ 4 = 8

Number of cupcakes that Paul had at first
= 8 u
= 8 x 8
= 64 

(b)
Total number of cupcakes that the 3 of them bought
= 8 u + 12 u + 3 u + 6
= 23 u + 6
= 23 x 8 + 6
= 184 + 6
= 190

Answer(s): (a) 64; (b) 190