Three girls, Gabby, Zara and Xylia had a total of 2880 beads. Some exchanges were made. First, Gabby gave Zara as many beads as Zara had. After that, Zara gave
13 of whatever she had then to Xylia. Finally, Xylia gave
14 of whatever she had to Gabby. As a result, they each had the same number of beads. How many beads did Gabby have at first?
|
Gabby |
Zara |
Xylia |
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 Gabby had at first
= 1 group - 1 box + 1 u
= 960 - 320 + 720
= 1360
Answer(s): 1360