Three girls, Jen, Ivory and Cathy had a total of 1260 coins. Some exchanges were made. First, Jen gave Ivory as many coins as Ivory had. After that, Ivory gave
14 of whatever she had then to Cathy. Finally, Cathy gave
15 of whatever she had to Jen. As a result, they each had the same number of coins. How many coins did Jen have at first?
|
Jen |
Ivory |
Cathy |
Total |
Before 1 |
? |
1 u |
|
1260 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
1260 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
5 boxes |
1260 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1260 |
3 groups = 1260
1 group = 1260 ÷ 3 = 420
1 group = 4 boxes 4 boxes = 420
1 box = 420 ÷ 4 = 105
3 p = 1 group
1 p = 420 ÷ 3 = 140
4 p = 4 x 140 = 560
4 p = 2 u
2 u = 560
1 u = 560 ÷ 2 = 280
Number of coins that Jen had at first
= 1 group - 1 box + 1 u
= 420 - 105 + 280
= 595
Answer(s): 595