Glen had three boxes, containing a total of 1650 styrofoam cups. The number of styrofoam cups in Box P to the total number of styrofoam cups was 3 : 11. He sold 331 styrofoam cups from Box Q and sold ¹₃ of the styrofoam cups in Box R. The number of styrofoam cups left in Box Q to the number of styrofoam cups left in Box R was 4 : 1. How many styrofoam cups were there in Box Q at first?

	Box P	Box Q	Box R	Total
Before	3 u	8 u (1200)		11 u (1650)
		8 p + 331	3 p
Change		- 331	- 1 p
			2 p
After		4x2 = 8 p	1x2 = 2 p

11 u = 1650
1 u = 1650 ÷ 11 = 150

Number of styrofoam cups in Box Q and Box R at first
= 8 u
= 8 x 150
= 1200

The number of cups left in R is the repeated identity.
LCM of 1 and 2 = 2

8 p + 331 + 3 p = 1200
8 p + 3 p = 1200 - 331
11 p = 869

1 p = 869 ÷ 11 = 79

Number of cups in Box Q at first
= 8 p + 331
= 8 x 79 + 331
= 632 + 331
= 963

Answer(s):963