Jack had three boxes, containing a total of 1430 styrofoam bowls. The number of styrofoam bowls in Box P to the total number of styrofoam bowls was 3 : 11. He sold 275 styrofoam bowls from Box Q and sold ¹₃ of the styrofoam bowls in Box R. The number of styrofoam bowls left in Box Q to the number of styrofoam bowls left in Box R was 3 : 1. How many styrofoam bowls were there in Box Q at first?

	Box P	Box Q	Box R	Total
Before	3 u	8 u (1040)		11 u (1430)
		6 p + 275	3 p
Change		- 275	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

11 u = 1430
1 u = 1430 ÷ 11 = 130

Number of styrofoam bowls in Box Q and Box R at first
= 8 u
= 8 x 130
= 1040

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

6 p + 275 + 3 p = 1040
6 p + 3 p = 1040 - 275
9 p = 765

1 p = 765 ÷ 9 = 85

Number of bowls in Box Q at first
= 6 p + 275
= 6 x 85 + 275
= 510 + 275
= 785

Answer(s):785