Three girls, Jen, Rachel and Nora had a total of 630 coins. Some exchanges were made. First, Jen gave Rachel as many coins as Rachel had. After that, Rachel gave
14 of whatever she had then to Nora. Finally, Nora gave
13 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 |
Rachel |
Nora |
Total |
Before 1 |
? |
1 u |
|
630 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
630 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
3 boxes |
630 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
630 |
3 groups = 630
1 group = 630 ÷ 3 = 210
1 group = 2 boxes 2 boxes = 210
1 box = 210 ÷ 2 = 105
3 p = 1 group
1 p = 210 ÷ 3 = 70
4 p = 4 x 70 = 280
4 p = 2 u
2 u = 280
1 u = 280 ÷ 2 = 140
Number of coins that Jen had at first
= 1 group - 1 box + 1 u
= 210 - 105 + 140
= 245
Answer(s): 245