Three girls, Gillian, Zoe and Betty had a total of 720 coins. Some exchanges were made. First, Gillian gave Zoe as many coins as Zoe had. After that, Zoe gave
14 of whatever she had then to Betty. Finally, Betty gave
14 of whatever she had to Gillian. As a result, they each had the same number of coins. How many coins did Gillian have at first?
|
Gillian |
Zoe |
Betty |
Total |
Before 1 |
? |
1 u |
|
720 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
720 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
4 boxes |
720 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
720 |
3 groups = 720
1 group = 720 ÷ 3 = 240
1 group = 3 boxes 3 boxes = 240
1 box = 240 ÷ 3 = 80
3 p = 1 group
1 p = 240 ÷ 3 = 80
4 p = 4 x 80 = 320
4 p = 2 u
2 u = 320
1 u = 320 ÷ 2 = 160
Number of coins that Gillian had at first
= 1 group - 1 box + 1 u
= 240 - 80 + 160
= 320
Answer(s): 320