Three girls, Cathy, Yoko and Risa had a total of 420 pens. Some exchanges were made. First, Cathy gave Yoko as many pens as Yoko had. After that, Yoko gave
13 of whatever she had then to Risa. Finally, Risa gave
13 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 |
Yoko |
Risa |
Total |
Before 1 |
? |
1 u |
|
420 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
420 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
420 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
420 |
3 groups = 420
1 group = 420 ÷ 3 = 140
1 group = 2 boxes 2 boxes = 140
1 box = 140 ÷ 2 = 70
2 p = 1 group
1 p = 140 ÷ 2 = 70
3 p = 3 x 70 = 210
3 p = 2 u
2 u = 210
1 u = 210 ÷ 2 = 105
Number of pens that Cathy had at first
= 1 group - 1 box + 1 u
= 140 - 70 + 105
= 175
Answer(s): 175