George had three boxes, containing a total of 1100 paper bowls. The number of paper bowls in Box T to the total number of paper bowls was 3 : 11. He sold 268 paper bowls from Box U and sold ¹₄ of the paper bowls in Box V. The number of paper bowls left in Box U to the number of paper bowls left in Box V was 5 : 1. How many paper bowls were there in Box U at first?

	Box T	Box U	Box V	Total
Before	3 u	8 u (800)		11 u (1100)
		15 p + 268	4 p
Change		- 268	- 1 p
			3 p
After		5x3 = 15 p	1x3 = 3 p

11 u = 1100
1 u = 1100 ÷ 11 = 100

Number of paper bowls in Box U and Box V at first
= 8 u
= 8 x 100
= 800

The number of bowls left in V is the repeated identity.
LCM of 1 and 3 = 3

15 p + 268 + 4 p = 800
15 p + 4 p = 800 - 268
19 p = 532

1 p = 532 ÷ 19 = 28

Number of bowls in Box U at first
= 15 p + 268
= 15 x 28 + 268
= 420 + 268
= 688

Answer(s):688