Three girls, Yen, Natalie and Nicole had a total of 4920 coins. Some exchanges were made. First, Yen gave Natalie as many coins as Natalie had. After that, Natalie gave
13 of whatever she had then to Nicole. Finally, Nicole 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 |
Natalie |
Nicole |
Total |
Before 1 |
? |
1 u |
|
4920 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
4920 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
4920 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4920 |
3 groups = 4920
1 group = 4920 ÷ 3 = 1640
1 group = 4 boxes 4 boxes = 1640
1 box = 1640 ÷ 4 = 410
2 p = 1 group
1 p = 1640 ÷ 2 = 820
3 p = 3 x 820 = 2460
3 p = 2 u
2 u = 2460
1 u = 2460 ÷ 2 = 1230
Number of coins that Yen had at first
= 1 group - 1 box + 1 u
= 1640 - 410 + 1230
= 2460
Answer(s): 2460