Three girls, Anna, Fanny and Sarah had a total of 5400 beads. Some exchanges were made. First, Anna gave Fanny as many beads as Fanny had. After that, Fanny gave
13 of whatever she had then to Sarah. Finally, Sarah gave
13 of whatever she had to Anna. As a result, they each had the same number of beads. How many beads did Anna have at first?
|
Anna |
Fanny |
Sarah |
Total |
Before 1 |
? |
1 u |
|
5400 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5400 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
5400 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5400 |
3 groups = 5400
1 group = 5400 ÷ 3 = 1800
1 group = 2 boxes 2 boxes = 1800
1 box = 1800 ÷ 2 = 900
2 p = 1 group
1 p = 1800 ÷ 2 = 900
3 p = 3 x 900 = 2700
3 p = 2 u
2 u = 2700
1 u = 2700 ÷ 2 = 1350
Number of beads that Anna had at first
= 1 group - 1 box + 1 u
= 1800 - 900 + 1350
= 2250
Answer(s): 2250