Three girls, Diana, Elyse and Natalie had a total of 4260 beads. Some exchanges were made. First, Diana gave Elyse as many beads as Elyse had. After that, Elyse gave
13 of whatever she had then to Natalie. Finally, Natalie gave
15 of whatever she had to Diana. As a result, they each had the same number of beads. How many beads did Diana have at first?
|
Diana |
Elyse |
Natalie |
Total |
Before 1 |
? |
1 u |
|
4260 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
4260 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
4260 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4260 |
3 groups = 4260
1 group = 4260 ÷ 3 = 1420
1 group = 4 boxes 4 boxes = 1420
1 box = 1420 ÷ 4 = 355
2 p = 1 group
1 p = 1420 ÷ 2 = 710
3 p = 3 x 710 = 2130
3 p = 2 u
2 u = 2130
1 u = 2130 ÷ 2 = 1065
Number of beads that Diana had at first
= 1 group - 1 box + 1 u
= 1420 - 355 + 1065
= 2130
Answer(s): 2130