Three girls, Lucy, Betty and Anna had a total of 4500 coins. Some exchanges were made. First, Lucy gave Betty as many coins as Betty had. After that, Betty gave
13 of whatever she had then to Anna. Finally, Anna gave
14 of whatever she had to Lucy. As a result, they each had the same number of coins. How many coins did Lucy have at first?
|
Lucy |
Betty |
Anna |
Total |
Before 1 |
? |
1 u |
|
4500 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
4500 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
4500 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4500 |
3 groups = 4500
1 group = 4500 ÷ 3 = 1500
1 group = 3 boxes 3 boxes = 1500
1 box = 1500 ÷ 3 = 500
2 p = 1 group
1 p = 1500 ÷ 2 = 750
3 p = 3 x 750 = 2250
3 p = 2 u
2 u = 2250
1 u = 2250 ÷ 2 = 1125
Number of coins that Lucy had at first
= 1 group - 1 box + 1 u
= 1500 - 500 + 1125
= 2125
Answer(s): 2125