Daniel had three boxes, containing a total of 1200 plastic plates. The number of plastic plates in Box N to the total number of plastic plates was 3 : 10. He sold 343 plastic plates from Box P and sold
13 of the plastic plates in Box Q. The number of plastic plates left in Box P to the number of plastic plates left in Box Q was 2 : 1. How many plastic plates were there in Box P at first?
|
Box N |
Box P |
Box Q |
Total |
Before |
3 u
|
7 u (840)
|
10 u (1200) |
|
|
4 p + 343 |
3 p |
|
Change |
|
- 343 |
- 1 p |
|
|
|
|
2 p |
|
After |
|
2x2 = 4 p |
1x2 = 2 p |
|
10 u = 1200
1 u = 1200 ÷ 10 = 120
Number of plastic plates in Box P and Box Q at first
= 7 u
= 7 x 120
= 840
The number of plates left in Q is the repeated identity.
LCM of 1 and 2 = 2
4 p + 343 + 3 p = 840
4 p + 3 p = 840 - 343
7 p = 497
1 p = 497 ÷ 7 = 71
Number of plates in Box P at first
= 4 p + 343
= 4 x 71 + 343
= 284 + 343
= 627
Answer(s):627