Three girls, Yen, Nora and Jen had a total of 1680 coins. Some exchanges were made. First, Yen gave Nora as many coins as Nora had. After that, Nora gave
13 of whatever she had then to Jen. Finally, Jen gave
15 of whatever she had to Yen. As a result, they each had the same number of coins. How many coins did Yen have at first?
|
Yen |
Nora |
Jen |
Total |
Before 1 |
? |
1 u |
|
1680 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1680 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
1680 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1680 |
3 groups = 1680
1 group = 1680 ÷ 3 = 560
1 group = 4 boxes 4 boxes = 560
1 box = 560 ÷ 4 = 140
2 p = 1 group
1 p = 560 ÷ 2 = 280
3 p = 3 x 280 = 840
3 p = 2 u
2 u = 840
1 u = 840 ÷ 2 = 420
Number of coins that Yen had at first
= 1 group - 1 box + 1 u
= 560 - 140 + 420
= 840
Answer(s): 840