Three girls, Eva, Jen and Joelle had a total of 3420 cards. Some exchanges were made. First, Eva gave Jen as many cards as Jen had. After that, Jen gave
13 of whatever she had then to Joelle. Finally, Joelle gave
15 of whatever she had to Eva. As a result, they each had the same number of cards. How many cards did Eva have at first?
|
Eva |
Jen |
Joelle |
Total |
Before 1 |
? |
1 u |
|
3420 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
3420 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
3420 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3420 |
3 groups = 3420
1 group = 3420 ÷ 3 = 1140
1 group = 4 boxes 4 boxes = 1140
1 box = 1140 ÷ 4 = 285
2 p = 1 group
1 p = 1140 ÷ 2 = 570
3 p = 3 x 570 = 1710
3 p = 2 u
2 u = 1710
1 u = 1710 ÷ 2 = 855
Number of cards that Eva had at first
= 1 group - 1 box + 1 u
= 1140 - 285 + 855
= 1710
Answer(s): 1710