Cole had three boxes, containing a total of 990 plastic cups. The number of plastic cups in Box U to the total number of plastic cups was 3 : 11. He sold 369 plastic cups from Box V and sold
13 of the plastic cups in Box W. The number of plastic cups left in Box V to the number of plastic cups left in Box W was 3 : 1. How many plastic cups were there in Box V at first?
|
Box U |
Box V |
Box W |
Total |
Before |
3 u
|
8 u (720)
|
11 u (990) |
|
|
6 p + 369 |
3 p |
|
Change |
|
- 369 |
- 1 p |
|
|
|
|
2 p |
|
After |
|
3x2 = 6 p |
1x2 = 2 p |
|
11 u = 990
1 u = 990 ÷ 11 = 90
Number of plastic cups in Box V and Box W at first
= 8 u
= 8 x 90
= 720
The number of cups left in W is the repeated identity.
LCM of 1 and 2 = 2
6 p + 369 + 3 p = 720
6 p + 3 p = 720 - 369
9 p = 351
1 p = 351 ÷ 9 = 39
Number of cups in Box V at first
= 6 p + 369
= 6 x 39 + 369
= 234 + 369
= 603
Answer(s):603