Archie had three boxes, containing a total of 1210 plastic bowls. The number of plastic bowls in Box W to the total number of plastic bowls was 3 : 11. He sold 399 plastic bowls from Box X and sold ¹₃ of the plastic bowls in Box Y. The number of plastic bowls left in Box X to the number of plastic bowls left in Box Y was 5 : 1. How many plastic bowls were there in Box X at first?

	Box W	Box X	Box Y	Total
Before	3 u	8 u (880)		11 u (1210)
		10 p + 399	3 p
Change		- 399	- 1 p
			2 p
After		5x2 = 10 p	1x2 = 2 p

11 u = 1210
1 u = 1210 ÷ 11 = 110

Number of plastic bowls in Box X and Box Y at first
= 8 u
= 8 x 110
= 880

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

10 p + 399 + 3 p = 880
10 p + 3 p = 880 - 399
13 p = 481

1 p = 481 ÷ 13 = 37

Number of bowls in Box X at first
= 10 p + 399
= 10 x 37 + 399
= 370 + 399
= 769

Answer(s):769