Zeph had three boxes, containing a total of 960 paper plates. The number of paper plates in Box N to the total number of paper plates was 3 : 8. He sold 271 paper plates from Box P and sold
13 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 2 : 1. How many paper plates were there in Box P at first?
|
Box N |
Box P |
Box Q |
Total |
Before |
3 u
|
5 u (600)
|
8 u (960) |
|
|
4 p + 271 |
3 p |
|
Change |
|
- 271 |
- 1 p |
|
|
|
|
2 p |
|
After |
|
2x2 = 4 p |
1x2 = 2 p |
|
8 u = 960
1 u = 960 ÷ 8 = 120
Number of paper plates in Box P and Box Q at first
= 5 u
= 5 x 120
= 600
The number of plates left in Q is the repeated identity.
LCM of 1 and 2 = 2
4 p + 271 + 3 p = 600
4 p + 3 p = 600 - 271
7 p = 329
1 p = 329 ÷ 7 = 47
Number of plates in Box P at first
= 4 p + 271
= 4 x 47 + 271
= 188 + 271
= 459
Answer(s):459