Valen had three boxes, containing a total of 980 plastic cups. The number of plastic cups in Box R to the total number of plastic cups was 3 : 7. He sold 305 plastic cups from Box S and sold ¹₅ of the plastic cups in Box T. The number of plastic cups left in Box S to the number of plastic cups left in Box T was 3 : 1. How many plastic cups were there in Box S at first?

	Box R	Box S	Box T	Total
Before	3 u	4 u (560)		7 u (980)
		12 p + 305	5 p
Change		- 305	- 1 p
			4 p
After		3x4 = 12 p	1x4 = 4 p

7 u = 980
1 u = 980 ÷ 7 = 140

Number of plastic cups in Box S and Box T at first
= 4 u
= 4 x 140
= 560

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

12 p + 305 + 5 p = 560
12 p + 5 p = 560 - 305
17 p = 255

1 p = 255 ÷ 17 = 15

Number of cups in Box S at first
= 12 p + 305
= 12 x 15 + 305
= 180 + 305
= 485

Answer(s):485