Henry had three boxes, containing a total of 1200 styrofoam plates. The number of styrofoam plates in Box X to the total number of styrofoam plates was 3 : 10. He sold 460 styrofoam plates from Box Y and sold ¹₄ of the styrofoam plates in Box Z. The number of styrofoam plates left in Box Y to the number of styrofoam plates left in Box Z was 2 : 1. How many styrofoam plates were there in Box Y at first?

	Box X	Box Y	Box Z	Total
Before	3 u	7 u (840)		10 u (1200)
		6 p + 460	4 p
Change		- 460	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

10 u = 1200
1 u = 1200 ÷ 10 = 120

Number of styrofoam plates in Box Y and Box Z at first
= 7 u
= 7 x 120
= 840

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

6 p + 460 + 4 p = 840
6 p + 4 p = 840 - 460
10 p = 380

1 p = 380 ÷ 10 = 38

Number of plates in Box Y at first
= 6 p + 460
= 6 x 38 + 460
= 228 + 460
= 688

Answer(s):688