Albert had three boxes, containing a total of 1400 styrofoam bowls. The number of styrofoam bowls in Box P to the total number of styrofoam bowls was 3 : 10. He sold 422 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	7 u (980)		10 u (1400)
		6 p + 422	3 p
Change		- 422	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

10 u = 1400
1 u = 1400 ÷ 10 = 140

Number of styrofoam bowls in Box Q and Box R at first
= 7 u
= 7 x 140
= 980

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

6 p + 422 + 3 p = 980
6 p + 3 p = 980 - 422
9 p = 558

1 p = 558 ÷ 9 = 62

Number of bowls in Box Q at first
= 6 p + 422
= 6 x 62 + 422
= 372 + 422
= 794

Answer(s):794