Elijah had three boxes, containing a total of 1100 styrofoam cups. The number of styrofoam cups in Box N to the total number of styrofoam cups was 3 : 10. He sold 306 styrofoam cups from Box P and sold ¹₄ of the styrofoam cups in Box Q. The number of styrofoam cups left in Box P to the number of styrofoam cups left in Box Q was 4 : 1. How many styrofoam cups were there in Box P at first?

	Box N	Box P	Box Q	Total
Before	3 u	7 u (770)		10 u (1100)
		12 p + 306	4 p
Change		- 306	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

10 u = 1100
1 u = 1100 ÷ 10 = 110

Number of styrofoam cups in Box P and Box Q at first
= 7 u
= 7 x 110
= 770

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

12 p + 306 + 4 p = 770
12 p + 4 p = 770 - 306
16 p = 464

1 p = 464 ÷ 16 = 29

Number of cups in Box P at first
= 12 p + 306
= 12 x 29 + 306
= 348 + 306
= 654

Answer(s):654