Three girls, Xylia, Abi and Linda had a total of 1260 pens. Some exchanges were made. First, Xylia gave Abi as many pens as Abi had. After that, Abi gave
14 of whatever she had then to Linda. Finally, Linda gave
13 of whatever she had to Xylia. As a result, they each had the same number of pens. How many pens did Xylia have at first?
|
Xylia |
Abi |
Linda |
Total |
Before 1 |
? |
1 u |
|
1260 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
1260 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
3 boxes |
1260 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1260 |
3 groups = 1260
1 group = 1260 ÷ 3 = 420
1 group = 2 boxes 2 boxes = 420
1 box = 420 ÷ 2 = 210
3 p = 1 group
1 p = 420 ÷ 3 = 140
4 p = 4 x 140 = 560
4 p = 2 u
2 u = 560
1 u = 560 ÷ 2 = 280
Number of pens that Xylia had at first
= 1 group - 1 box + 1 u
= 420 - 210 + 280
= 490
Answer(s): 490