Three girls, Linda, Fiona and Vanessa had a total of 3420 cards. Some exchanges were made. First, Linda gave Fiona as many cards as Fiona had. After that, Fiona gave
14 of whatever she had then to Vanessa. Finally, Vanessa gave
14 of whatever she had to Linda. As a result, they each had the same number of cards. How many cards did Linda have at first?
|
Linda |
Fiona |
Vanessa |
Total |
Before 1 |
? |
1 u |
|
3420 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
3420 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
4 boxes |
3420 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3420 |
3 groups = 3420
1 group = 3420 ÷ 3 = 1140
1 group = 3 boxes 3 boxes = 1140
1 box = 1140 ÷ 3 = 380
3 p = 1 group
1 p = 1140 ÷ 3 = 380
4 p = 4 x 380 = 1520
4 p = 2 u
2 u = 1520
1 u = 1520 ÷ 2 = 760
Number of cards that Linda had at first
= 1 group - 1 box + 1 u
= 1140 - 380 + 760
= 1520
Answer(s): 1520