Three girls, Erika, Abi and Jaslyn had a total of 5040 cards. Some exchanges were made. First, Erika gave Abi as many cards as Abi had. After that, Abi gave
13 of whatever she had then to Jaslyn. Finally, Jaslyn gave
15 of whatever she had to Erika. As a result, they each had the same number of cards. How many cards did Erika have at first?
|
Erika |
Abi |
Jaslyn |
Total |
Before 1 |
? |
1 u |
|
5040 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5040 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
5040 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5040 |
3 groups = 5040
1 group = 5040 ÷ 3 = 1680
1 group = 4 boxes 4 boxes = 1680
1 box = 1680 ÷ 4 = 420
2 p = 1 group
1 p = 1680 ÷ 2 = 840
3 p = 3 x 840 = 2520
3 p = 2 u
2 u = 2520
1 u = 2520 ÷ 2 = 1260
Number of cards that Erika had at first
= 1 group - 1 box + 1 u
= 1680 - 420 + 1260
= 2520
Answer(s): 2520