Jeremy had three boxes, containing a total of 1320 paper bowls. The number of paper bowls in Box T to the total number of paper bowls was 3 : 11. He sold 401 paper bowls from Box U and sold ¹₃ 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 (960)		11 u (1320)
		10 p + 401	3 p
Change		- 401	- 1 p
			2 p
After		5x2 = 10 p	1x2 = 2 p

11 u = 1320
1 u = 1320 ÷ 11 = 120

Number of paper bowls in Box U and Box V at first
= 8 u
= 8 x 120
= 960

The number of bowls left in V is the repeated identity.
LCM of 1 and 2 = 2

10 p + 401 + 3 p = 960
10 p + 3 p = 960 - 401
13 p = 559

1 p = 559 ÷ 13 = 43

Number of bowls in Box U at first
= 10 p + 401
= 10 x 43 + 401
= 430 + 401
= 831

Answer(s):831