Three girls, Emma, Eva and Olivia had a total of 1320 coins. Some exchanges were made. First, Emma gave Eva as many coins as Eva had. After that, Eva gave
15 of whatever she had then to Olivia. Finally, Olivia gave
15 of whatever she had to Emma. As a result, they each had the same number of coins. How many coins did Emma have at first?
|
Emma |
Eva |
Olivia |
Total |
Before 1 |
? |
1 u |
|
1320 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
1320 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
5 boxes |
1320 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1320 |
3 groups = 1320
1 group = 1320 ÷ 3 = 440
1 group = 4 boxes 4 boxes = 440
1 box = 440 ÷ 4 = 110
4 p = 1 group
1 p = 440 ÷ 4 = 110
5 p = 5 x 110 = 550
5 p = 2 u
2 u = 550
1 u = 550 ÷ 2 = 275
Number of coins that Emma had at first
= 1 group - 1 box + 1 u
= 440 - 110 + 275
= 605
Answer(s): 605