Billy had three boxes, containing a total of 880 styrofoam cups. The number of styrofoam cups in Box R to the total number of styrofoam cups was 3 : 8. He sold 500 styrofoam cups from Box S and sold ¹₅ of the styrofoam cups in Box T. The number of styrofoam cups left in Box S to the number of styrofoam cups left in Box T was 5 : 1. How many styrofoam cups were there in Box S at first?

	Box R	Box S	Box T	Total
Before	3 u	5 u (550)		8 u (880)
		20 p + 500	5 p
Change		- 500	- 1 p
			4 p
After		5x4 = 20 p	1x4 = 4 p

8 u = 880
1 u = 880 ÷ 8 = 110

Number of styrofoam cups in Box S and Box T at first
= 5 u
= 5 x 110
= 550

The number of cups left in T is the repeated identity.
LCM of 1 and 4 = 4

20 p + 500 + 5 p = 550
20 p + 5 p = 550 - 500
25 p = 50

1 p = 50 ÷ 25 = 2

Number of cups in Box S at first
= 20 p + 500
= 20 x 2 + 500
= 40 + 500
= 540

Answer(s):540