Archie had three boxes, containing a total of 720 paper bowls. The number of paper bowls in Box H to the total number of paper bowls was 3 : 8. He sold 346 paper bowls from Box J and sold ¹₃ of the paper bowls in Box K. The number of paper bowls left in Box J to the number of paper bowls left in Box K was 5 : 1. How many paper bowls were there in Box J at first?

	Box H	Box J	Box K	Total
Before	3 u	5 u (450)		8 u (720)
		10 p + 346	3 p
Change		- 346	- 1 p
			2 p
After		5x2 = 10 p	1x2 = 2 p

8 u = 720
1 u = 720 ÷ 8 = 90

Number of paper bowls in Box J and Box K at first
= 5 u
= 5 x 90
= 450

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

10 p + 346 + 3 p = 450
10 p + 3 p = 450 - 346
13 p = 104

1 p = 104 ÷ 13 = 8

Number of bowls in Box J at first
= 10 p + 346
= 10 x 8 + 346
= 80 + 346
= 426

Answer(s):426