Simon had three boxes, containing a total of 1100 plastic cups. The number of plastic cups in Box M to the total number of plastic cups was 3 : 11. He sold 432 plastic cups from Box N and sold ¹₄ of the plastic cups in Box P. The number of plastic cups left in Box N to the number of plastic cups left in Box P was 4 : 1. How many plastic cups were there in Box N at first?

	Box M	Box N	Box P	Total
Before	3 u	8 u (800)		11 u (1100)
		12 p + 432	4 p
Change		- 432	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

11 u = 1100
1 u = 1100 ÷ 11 = 100

Number of plastic cups in Box N and Box P at first
= 8 u
= 8 x 100
= 800

The number of cups left in P is the repeated identity.
LCM of 1 and 3 = 3

12 p + 432 + 4 p = 800
12 p + 4 p = 800 - 432
16 p = 368

1 p = 368 ÷ 16 = 23

Number of cups in Box N at first
= 12 p + 432
= 12 x 23 + 432
= 276 + 432
= 708

Answer(s):708