Three girls, Hazel, Erika and Elyse had a total of 2970 coins. Some exchanges were made. First, Hazel gave Erika as many coins as Erika had. After that, Erika gave
14 of whatever she had then to Elyse. Finally, Elyse gave
14 of whatever she had to Hazel. As a result, they each had the same number of coins. How many coins did Hazel have at first?
|
Hazel |
Erika |
Elyse |
Total |
Before 1 |
? |
1 u |
|
2970 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
2970 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
4 boxes |
2970 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2970 |
3 groups = 2970
1 group = 2970 ÷ 3 = 990
1 group = 3 boxes 3 boxes = 990
1 box = 990 ÷ 3 = 330
3 p = 1 group
1 p = 990 ÷ 3 = 330
4 p = 4 x 330 = 1320
4 p = 2 u
2 u = 1320
1 u = 1320 ÷ 2 = 660
Number of coins that Hazel had at first
= 1 group - 1 box + 1 u
= 990 - 330 + 660
= 1320
Answer(s): 1320