Oliver had three boxes, containing a total of 980 styrofoam cups. The number of styrofoam cups in Box S to the total number of styrofoam cups was 3 : 7. He sold 351 styrofoam cups from Box T and sold ¹₄ of the styrofoam cups in Box U. The number of styrofoam cups left in Box T to the number of styrofoam cups left in Box U was 5 : 1. How many styrofoam cups were there in Box T at first?

	Box S	Box T	Box U	Total
Before	3 u	4 u (560)		7 u (980)
		15 p + 351	4 p
Change		- 351	- 1 p
			3 p
After		5x3 = 15 p	1x3 = 3 p

7 u = 980
1 u = 980 ÷ 7 = 140

Number of styrofoam cups in Box T and Box U at first
= 4 u
= 4 x 140
= 560

The number of cups left in U is the repeated identity.
LCM of 1 and 3 = 3

15 p + 351 + 4 p = 560
15 p + 4 p = 560 - 351
19 p = 209

1 p = 209 ÷ 19 = 11

Number of cups in Box T at first
= 15 p + 351
= 15 x 11 + 351
= 165 + 351
= 516

Answer(s):516