Three girls, Opal, Wendy and Jean had a total of 2880 beads. Some exchanges were made. First, Opal gave Wendy as many beads as Wendy had. After that, Wendy gave
13 of whatever she had then to Jean. Finally, Jean gave
14 of whatever she had to Opal. As a result, they each had the same number of beads. How many beads did Opal have at first?
|
Opal |
Wendy |
Jean |
Total |
Before 1 |
? |
1 u |
|
2880 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
2880 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
2880 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2880 |
3 groups = 2880
1 group = 2880 ÷ 3 = 960
1 group = 3 boxes 3 boxes = 960
1 box = 960 ÷ 3 = 320
2 p = 1 group
1 p = 960 ÷ 2 = 480
3 p = 3 x 480 = 1440
3 p = 2 u
2 u = 1440
1 u = 1440 ÷ 2 = 720
Number of beads that Opal had at first
= 1 group - 1 box + 1 u
= 960 - 320 + 720
= 1360
Answer(s): 1360