Three girls, Abi, Diana and Erika had a total of 5340 beads. Some exchanges were made. First, Abi gave Diana as many beads as Diana had. After that, Diana gave
13 of whatever she had then to Erika. Finally, Erika gave
15 of whatever she had to Abi. As a result, they each had the same number of beads. How many beads did Abi have at first?
|
Abi |
Diana |
Erika |
Total |
Before 1 |
? |
1 u |
|
5340 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5340 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
5340 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5340 |
3 groups = 5340
1 group = 5340 ÷ 3 = 1780
1 group = 4 boxes 4 boxes = 1780
1 box = 1780 ÷ 4 = 445
2 p = 1 group
1 p = 1780 ÷ 2 = 890
3 p = 3 x 890 = 2670
3 p = 2 u
2 u = 2670
1 u = 2670 ÷ 2 = 1335
Number of beads that Abi had at first
= 1 group - 1 box + 1 u
= 1780 - 445 + 1335
= 2670
Answer(s): 2670