Three girls, Kathy, Nora and Eva had a total of 1620 erasers. Some exchanges were made. First, Kathy gave Nora as many erasers as Nora had. After that, Nora gave
13 of whatever she had then to Eva. Finally, Eva gave
15 of whatever she had to Kathy. As a result, they each had the same number of erasers. How many erasers did Kathy have at first?
|
Kathy |
Nora |
Eva |
Total |
Before 1 |
? |
1 u |
|
1620 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1620 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
1620 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1620 |
3 groups = 1620
1 group = 1620 ÷ 3 = 540
1 group = 4 boxes 4 boxes = 540
1 box = 540 ÷ 4 = 135
2 p = 1 group
1 p = 540 ÷ 2 = 270
3 p = 3 x 270 = 810
3 p = 2 u
2 u = 810
1 u = 810 ÷ 2 = 405
Number of erasers that Kathy had at first
= 1 group - 1 box + 1 u
= 540 - 135 + 405
= 810
Answer(s): 810