Seth had three boxes, containing a total of 1120 styrofoam bowls. The number of styrofoam bowls in Box J to the total number of styrofoam bowls was 3 : 8. He sold 460 styrofoam bowls from Box K and sold ¹₄ of the styrofoam bowls in Box L. The number of styrofoam bowls left in Box K to the number of styrofoam bowls left in Box L was 2 : 1. How many styrofoam bowls were there in Box K at first?

	Box J	Box K	Box L	Total
Before	3 u	5 u (700)		8 u (1120)
		6 p + 460	4 p
Change		- 460	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

8 u = 1120
1 u = 1120 ÷ 8 = 140

Number of styrofoam bowls in Box K and Box L at first
= 5 u
= 5 x 140
= 700

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

6 p + 460 + 4 p = 700
6 p + 4 p = 700 - 460
10 p = 240

1 p = 240 ÷ 10 = 24

Number of bowls in Box K at first
= 6 p + 460
= 6 x 24 + 460
= 144 + 460
= 604

Answer(s):604