Brandon had three boxes, containing a total of 630 plastic cups. The number of plastic cups in Box D to the total number of plastic cups was 3 : 7. He sold 276 plastic cups from Box E and sold
13 of the plastic cups in Box F. The number of plastic cups left in Box E to the number of plastic cups left in Box F was 2 : 1. How many plastic cups were there in Box E at first?
|
Box D |
Box E |
Box F |
Total |
Before |
3 u
|
4 u (360)
|
7 u (630) |
|
|
4 p + 276 |
3 p |
|
Change |
|
- 276 |
- 1 p |
|
|
|
|
2 p |
|
After |
|
2x2 = 4 p |
1x2 = 2 p |
|
7 u = 630
1 u = 630 ÷ 7 = 90
Number of plastic cups in Box E and Box F at first
= 4 u
= 4 x 90
= 360
The number of cups left in F is the repeated identity.
LCM of 1 and 2 = 2
4 p + 276 + 3 p = 360
4 p + 3 p = 360 - 276
7 p = 84
1 p = 84 ÷ 7 = 12
Number of cups in Box E at first
= 4 p + 276
= 4 x 12 + 276
= 48 + 276
= 324
Answer(s):324