Nick had three boxes, containing a total of 990 styrofoam cups. The number of styrofoam cups in Box S to the total number of styrofoam cups was 3 : 11. He sold 351 styrofoam cups from Box T and sold
13 of the styrofoam cups in Box U. The number of styrofoam cups left in Box T to the number of styrofoam cups left in Box U was 3 : 1. How many styrofoam cups were there in Box T at first?
|
Box S |
Box T |
Box U |
Total |
Before |
3 u
|
8 u (720)
|
11 u (990) |
|
|
6 p + 351 |
3 p |
|
Change |
|
- 351 |
- 1 p |
|
|
|
|
2 p |
|
After |
|
3x2 = 6 p |
1x2 = 2 p |
|
11 u = 990
1 u = 990 ÷ 11 = 90
Number of styrofoam cups in Box T and Box U at first
= 8 u
= 8 x 90
= 720
The number of cups left in U is the repeated identity.
LCM of 1 and 2 = 2
6 p + 351 + 3 p = 720
6 p + 3 p = 720 - 351
9 p = 369
1 p = 369 ÷ 9 = 41
Number of cups in Box T at first
= 6 p + 351
= 6 x 41 + 351
= 246 + 351
= 597
Answer(s):597