Luke, Ken and Ryan bought some cookies. After Luke ate ²₅ of his cookies, Ken ate ²₃ of his cookies and Ryan ate 7 cookies, each of them had the same number of cookies left. Luke had 32 less cookies than Ken at first.

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

	Luke	Ken	Ryan
Before	5 u	3x3 = 9 u	3 u + 7
Change	- 2 u	- 2x3 = - 6 u	- 7
After	3 u	1x3 = 3 u	3 u

(a)
The number of cookies that Luke and Ken each had in the end is the same. Make the number of cookies that Luke and Ken each had in the end the same.  LCM of 3 and 1 is 3.

Number of cookies that Luke had less than Ken at first
= 9 u - 5 u
= 4 u

4 u = 32

1 u = 32 ÷ 4 = 8

Number of cookies that Luke had at first
= 5 u
= 5 x 8
= 40 

(b)
Total number of cookies that the 3 of them bought
= 5 u + 9 u + 3 u + 7
= 17 u + 7
= 17 x 8 + 7
= 136 + 7
= 143

Answer(s): (a) 40; (b) 143