Howard had three boxes, containing a total of 560 paper cups. The number of paper cups in Box S to the total number of paper cups was 3 : 7. He sold 272 paper cups from Box T and sold ¹₄ of the paper cups in Box U. The number of paper cups left in Box T to the number of paper cups left in Box U was 4 : 1. How many paper cups were there in Box T at first?

	Box S	Box T	Box U	Total
Before	3 u	4 u (320)		7 u (560)
		12 p + 272	4 p
Change		- 272	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

7 u = 560
1 u = 560 ÷ 7 = 80

Number of paper cups in Box T and Box U at first
= 4 u
= 4 x 80
= 320

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

12 p + 272 + 4 p = 320
12 p + 4 p = 320 - 272
16 p = 48

1 p = 48 ÷ 16 = 3

Number of cups in Box T at first
= 12 p + 272
= 12 x 3 + 272
= 36 + 272
= 308

Answer(s):308