Bobby had three boxes, containing a total of 1040 paper bowls. The number of paper bowls in Box P to the total number of paper bowls was 3 : 8. He sold 299 paper bowls from Box Q and sold ¹₃ of the paper bowls in Box R. The number of paper bowls left in Box Q to the number of paper bowls left in Box R was 3 : 1. How many paper bowls were there in Box Q at first?

	Box P	Box Q	Box R	Total
Before	3 u	5 u (650)		8 u (1040)
		6 p + 299	3 p
Change		- 299	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

8 u = 1040
1 u = 1040 ÷ 8 = 130

Number of paper bowls in Box Q and Box R at first
= 5 u
= 5 x 130
= 650

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

6 p + 299 + 3 p = 650
6 p + 3 p = 650 - 299
9 p = 351

1 p = 351 ÷ 9 = 39

Number of bowls in Box Q at first
= 6 p + 299
= 6 x 39 + 299
= 234 + 299
= 533

Answer(s):533