Three girls, Cindy, Wendy and Xylia had a total of 960 erasers. Some exchanges were made. First, Cindy gave Wendy as many erasers as Wendy had. After that, Wendy gave
13 of whatever she had then to Xylia. Finally, Xylia gave
13 of whatever she had to Cindy. As a result, they each had the same number of erasers. How many erasers did Cindy have at first?
|
Cindy |
Wendy |
Xylia |
Total |
Before 1 |
? |
1 u |
|
960 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
960 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
960 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
960 |
3 groups = 960
1 group = 960 ÷ 3 = 320
1 group = 2 boxes 2 boxes = 320
1 box = 320 ÷ 2 = 160
2 p = 1 group
1 p = 320 ÷ 2 = 160
3 p = 3 x 160 = 480
3 p = 2 u
2 u = 480
1 u = 480 ÷ 2 = 240
Number of erasers that Cindy had at first
= 1 group - 1 box + 1 u
= 320 - 160 + 240
= 400
Answer(s): 400