Nick had three boxes, containing a total of 1400 paper plates. The number of paper plates in Box T to the total number of paper plates was 3 : 10. He sold 499 paper plates from Box U and sold ¹₄ of the paper plates in Box V. The number of paper plates left in Box U to the number of paper plates left in Box V was 3 : 1. How many paper plates were there in Box U at first?

	Box T	Box U	Box V	Total
Before	3 u	7 u (980)		10 u (1400)
		9 p + 499	4 p
Change		- 499	- 1 p
			3 p
After		3x3 = 9 p	1x3 = 3 p

10 u = 1400
1 u = 1400 ÷ 10 = 140

Number of paper plates in Box U and Box V at first
= 7 u
= 7 x 140
= 980

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

9 p + 499 + 4 p = 980
9 p + 4 p = 980 - 499
13 p = 481

1 p = 481 ÷ 13 = 37

Number of plates in Box U at first
= 9 p + 499
= 9 x 37 + 499
= 333 + 499
= 832

Answer(s):832