Wesley had three boxes, containing a total of 700 paper plates. The number of paper plates in Box X to the total number of paper plates was 3 : 7. He sold 257 paper plates from Box Y and sold ¹₅ of the paper plates in Box Z. The number of paper plates left in Box Y to the number of paper plates left in Box Z was 2 : 1. How many paper plates were there in Box Y at first?

	Box X	Box Y	Box Z	Total
Before	3 u	4 u (400)		7 u (700)
		8 p + 257	5 p
Change		- 257	- 1 p
			4 p
After		2x4 = 8 p	1x4 = 4 p

7 u = 700
1 u = 700 ÷ 7 = 100

Number of paper plates in Box Y and Box Z at first
= 4 u
= 4 x 100
= 400

The number of plates left in Z is the repeated identity.
LCM of 1 and 4 = 4

8 p + 257 + 5 p = 400
8 p + 5 p = 400 - 257
13 p = 143

1 p = 143 ÷ 13 = 11

Number of plates in Box Y at first
= 8 p + 257
= 8 x 11 + 257
= 88 + 257
= 345

Answer(s):345