Three girls, Xandra, Gabby and Nicole had a total of 2880 beads. Some exchanges were made. First, Xandra gave Gabby as many beads as Gabby had. After that, Gabby gave
14 of whatever she had then to Nicole. Finally, Nicole gave
13 of whatever she had to Xandra. As a result, they each had the same number of beads. How many beads did Xandra have at first?
|
Xandra |
Gabby |
Nicole |
Total |
Before 1 |
? |
1 u |
|
2880 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
2880 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
3 boxes |
2880 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2880 |
3 groups = 2880
1 group = 2880 ÷ 3 = 960
1 group = 2 boxes 2 boxes = 960
1 box = 960 ÷ 2 = 480
3 p = 1 group
1 p = 960 ÷ 3 = 320
4 p = 4 x 320 = 1280
4 p = 2 u
2 u = 1280
1 u = 1280 ÷ 2 = 640
Number of beads that Xandra had at first
= 1 group - 1 box + 1 u
= 960 - 480 + 640
= 1120
Answer(s): 1120