Perry had three boxes, containing a total of 1300 paper bowls. The number of paper bowls in Box R to the total number of paper bowls was 3 : 10. He sold 446 paper bowls from Box S and sold ¹₄ of the paper bowls in Box T. The number of paper bowls left in Box S to the number of paper bowls left in Box T was 4 : 1. How many paper bowls were there in Box S at first?

	Box R	Box S	Box T	Total
Before	3 u	7 u (910)		10 u (1300)
		12 p + 446	4 p
Change		- 446	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

10 u = 1300
1 u = 1300 ÷ 10 = 130

Number of paper bowls in Box S and Box T at first
= 7 u
= 7 x 130
= 910

The number of bowls left in T is the repeated identity.
LCM of 1 and 3 = 3

12 p + 446 + 4 p = 910
12 p + 4 p = 910 - 446
16 p = 464

1 p = 464 ÷ 16 = 29

Number of bowls in Box S at first
= 12 p + 446
= 12 x 29 + 446
= 348 + 446
= 794

Answer(s):794