Tom, Vincent and Pierre bought some cookies. After Tom ate ³₇ of his cookies, Vincent ate ³₄ of his cookies and Pierre ate 6 cookies, each of them had the same number of cookies left. Tom had 54 less cookies than Vincent at first.

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

	Tom	Vincent	Pierre
Before	7 u	4x4 = 16 u	4 u + 6
Change	- 3 u	- 3x4 = - 12 u	- 6
After	4 u	1x4 = 4 u	4 u

(a)
The number of cookies that Tom and Vincent each had in the end is the same. Make the number of cookies that Tom and Vincent each had in the end the same.  LCM of 4 and 1 is 4.

Number of cookies that Tom had less than Vincent at first
= 16 u - 7 u
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Number of cookies that Tom had at first
= 7 u
= 7 x 6
= 42 

(b)
Total number of cookies that the 3 of them bought
= 7 u + 16 u + 4 u + 6
= 27 u + 6
= 27 x 6 + 6
= 162 + 6
= 168

Answer(s): (a) 42; (b) 168