Elijah had three boxes, containing a total of 660 styrofoam bowls. The number of styrofoam bowls in Box H to the total number of styrofoam bowls was 3 : 11. He sold 363 styrofoam bowls from Box J and sold ¹₃ of the styrofoam bowls in Box K. The number of styrofoam bowls left in Box J to the number of styrofoam bowls left in Box K was 5 : 1. How many styrofoam bowls were there in Box J at first?

	Box H	Box J	Box K	Total
Before	3 u	8 u (480)		11 u (660)
		10 p + 363	3 p
Change		- 363	- 1 p
			2 p
After		5x2 = 10 p	1x2 = 2 p

11 u = 660
1 u = 660 ÷ 11 = 60

Number of styrofoam bowls in Box J and Box K at first
= 8 u
= 8 x 60
= 480

The number of bowls left in K is the repeated identity.
LCM of 1 and 2 = 2

10 p + 363 + 3 p = 480
10 p + 3 p = 480 - 363
13 p = 117

1 p = 117 ÷ 13 = 9

Number of bowls in Box J at first
= 10 p + 363
= 10 x 9 + 363
= 90 + 363
= 453

Answer(s):453