Luke, Asher and Vincent bought some biscuits. After Luke ate ³₇ of his biscuits, Asher ate ⁴₅ of his biscuits and Vincent ate 2 biscuits, each of them had the same number of biscuits left. Luke had 104 less biscuits than Asher at first.

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

	Luke	Asher	Vincent
Before	7 u	5x4 = 20 u	4 u + 2
Change	- 3 u	- 4x4 = - 16 u	- 2
After	4 u	1x4 = 4 u	4 u

(a)
The number of biscuits that Luke and Asher each had in the end is the same. Make the number of biscuits that Luke and Asher each had in the end the same.  LCM of 4 and 1 is 4.

Number of biscuits that Luke had less than Asher at first
= 20 u - 7 u
= 13 u

13 u = 104

1 u = 104 ÷ 13 = 8

Number of biscuits that Luke had at first
= 7 u
= 7 x 8
= 56 

(b)
Total number of biscuits that the 3 of them bought
= 7 u + 20 u + 4 u + 2
= 31 u + 2
= 31 x 8 + 2
= 248 + 2
= 250

Answer(s): (a) 56; (b) 250