Three girls, Diana, Hazel and Abi had a total of 1200 cards. Some exchanges were made. First, Diana gave Hazel as many cards as Hazel had. After that, Hazel gave
13 of whatever she had then to Abi. Finally, Abi gave
13 of whatever she had to Diana. As a result, they each had the same number of cards. How many cards did Diana have at first?
|
Diana |
Hazel |
Abi |
Total |
Before 1 |
? |
1 u |
|
1200 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1200 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
1200 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1200 |
3 groups = 1200
1 group = 1200 ÷ 3 = 400
1 group = 2 boxes 2 boxes = 400
1 box = 400 ÷ 2 = 200
2 p = 1 group
1 p = 400 ÷ 2 = 200
3 p = 3 x 200 = 600
3 p = 2 u
2 u = 600
1 u = 600 ÷ 2 = 300
Number of cards that Diana had at first
= 1 group - 1 box + 1 u
= 400 - 200 + 300
= 500
Answer(s): 500