Pierre had three boxes, containing a total of 660 paper plates. The number of paper plates in Box N to the total number of paper plates was 3 : 11. He sold 272 paper plates from Box P and sold ¹₄ of the paper plates in Box Q. The number of paper plates left in Box P to the number of paper plates left in Box Q was 3 : 1. How many paper plates were there in Box P at first?

	Box N	Box P	Box Q	Total
Before	3 u	8 u (480)		11 u (660)
		9 p + 272	4 p
Change		- 272	- 1 p
			3 p
After		3x3 = 9 p	1x3 = 3 p

11 u = 660
1 u = 660 ÷ 11 = 60

Number of paper plates in Box P and Box Q at first
= 8 u
= 8 x 60
= 480

The number of plates left in Q is the repeated identity.
LCM of 1 and 3 = 3

9 p + 272 + 4 p = 480
9 p + 4 p = 480 - 272
13 p = 208

1 p = 208 ÷ 13 = 16

Number of plates in Box P at first
= 9 p + 272
= 9 x 16 + 272
= 144 + 272
= 416

Answer(s):416