Three girls, Xylia, Natalie and Eva had a total of 5760 marbles. Some exchanges were made. First, Xylia gave Natalie as many marbles as Natalie had. After that, Natalie gave
13 of whatever she had then to Eva. Finally, Eva gave
14 of whatever she had to Xylia. As a result, they each had the same number of marbles. How many marbles did Xylia have at first?
|
Xylia |
Natalie |
Eva |
Total |
Before 1 |
? |
1 u |
|
5760 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5760 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
5760 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5760 |
3 groups = 5760
1 group = 5760 ÷ 3 = 1920
1 group = 3 boxes 3 boxes = 1920
1 box = 1920 ÷ 3 = 640
2 p = 1 group
1 p = 1920 ÷ 2 = 960
3 p = 3 x 960 = 2880
3 p = 2 u
2 u = 2880
1 u = 2880 ÷ 2 = 1440
Number of marbles that Xylia had at first
= 1 group - 1 box + 1 u
= 1920 - 640 + 1440
= 2720
Answer(s): 2720