Perry had three boxes, containing a total of 960 styrofoam plates. The number of styrofoam plates in Box Q to the total number of styrofoam plates was 3 : 8. He sold 350 styrofoam plates from Box R and sold ¹₅ of the styrofoam plates in Box S. The number of styrofoam plates left in Box R to the number of styrofoam plates left in Box S was 5 : 1. How many styrofoam plates were there in Box R at first?

	Box Q	Box R	Box S	Total
Before	3 u	5 u (600)		8 u (960)
		20 p + 350	5 p
Change		- 350	- 1 p
			4 p
After		5x4 = 20 p	1x4 = 4 p

8 u = 960
1 u = 960 ÷ 8 = 120

Number of styrofoam plates in Box R and Box S at first
= 5 u
= 5 x 120
= 600

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

20 p + 350 + 5 p = 600
20 p + 5 p = 600 - 350
25 p = 250

1 p = 250 ÷ 25 = 10

Number of plates in Box R at first
= 20 p + 350
= 20 x 10 + 350
= 200 + 350
= 550

Answer(s):550