Luis, Oscar and Caden bought some cupcakes. After Luis ate ⁵₇ of his cupcakes, Oscar ate ³₄ of his cupcakes and Caden ate 6 cupcakes, each of them had the same number of cupcakes left. Luis had 5 less cupcakes than Oscar at first.

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

	Luis	Oscar	Caden
Before	7 u	4x2 = 8 u	2 u + 6
Change	- 5 u	- 3x2 = - 6 u	- 6
After	2 u	1x2 = 2 u	2 u

(a)
The number of cupcakes that Luis and Oscar each had in the end is the same. Make the number of cupcakes that Luis and Oscar each had in the end the same.  LCM of 2 and 1 is 2.

Number of cupcakes that Luis had less than Oscar at first
= 8 u - 7 u
= 1 u

1 u = 5

1 u = 5 ÷ 1 = 5

Number of cupcakes that Luis had at first
= 7 u
= 7 x 5
= 35 

(b)
Total number of cupcakes that the 3 of them bought
= 7 u + 8 u + 2 u + 6
= 17 u + 6
= 17 x 5 + 6
= 85 + 6
= 91

Answer(s): (a) 35; (b) 91