Three girls, Cathy, Xylia and Olivia had a total of 1260 pens. Some exchanges were made. First, Cathy gave Xylia as many pens as Xylia had. After that, Xylia gave
13 of whatever she had then to Olivia. Finally, Olivia gave
15 of whatever she had to Cathy. As a result, they each had the same number of pens. How many pens did Cathy have at first?
|
Cathy |
Xylia |
Olivia |
Total |
Before 1 |
? |
1 u |
|
1260 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1260 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
1260 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1260 |
3 groups = 1260
1 group = 1260 ÷ 3 = 420
1 group = 4 boxes 4 boxes = 420
1 box = 420 ÷ 4 = 105
2 p = 1 group
1 p = 420 ÷ 2 = 210
3 p = 3 x 210 = 630
3 p = 2 u
2 u = 630
1 u = 630 ÷ 2 = 315
Number of pens that Cathy had at first
= 1 group - 1 box + 1 u
= 420 - 105 + 315
= 630
Answer(s): 630