Three girls, Zara, Dana and Tiffany had a total of 3060 coins. Some exchanges were made. First, Zara gave Dana as many coins as Dana had. After that, Dana gave
13 of whatever she had then to Tiffany. Finally, Tiffany gave
14 of whatever she had to Zara. As a result, they each had the same number of coins. How many coins did Zara have at first?
|
Zara |
Dana |
Tiffany |
Total |
Before 1 |
? |
1 u |
|
3060 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
3060 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
3060 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3060 |
3 groups = 3060
1 group = 3060 ÷ 3 = 1020
1 group = 3 boxes 3 boxes = 1020
1 box = 1020 ÷ 3 = 340
2 p = 1 group
1 p = 1020 ÷ 2 = 510
3 p = 3 x 510 = 1530
3 p = 2 u
2 u = 1530
1 u = 1530 ÷ 2 = 765
Number of coins that Zara had at first
= 1 group - 1 box + 1 u
= 1020 - 340 + 765
= 1445
Answer(s): 1445