Three girls, Gwen, Penelope and Emily had a total of 2940 erasers. Some exchanges were made. First, Gwen gave Penelope as many erasers as Penelope had. After that, Penelope gave
13 of whatever she had then to Emily. Finally, Emily gave
13 of whatever she had to Gwen. As a result, they each had the same number of erasers. How many erasers did Gwen have at first?
|
Gwen |
Penelope |
Emily |
Total |
Before 1 |
? |
1 u |
|
2940 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
2940 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
2940 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2940 |
3 groups = 2940
1 group = 2940 ÷ 3 = 980
1 group = 2 boxes 2 boxes = 980
1 box = 980 ÷ 2 = 490
2 p = 1 group
1 p = 980 ÷ 2 = 490
3 p = 3 x 490 = 1470
3 p = 2 u
2 u = 1470
1 u = 1470 ÷ 2 = 735
Number of erasers that Gwen had at first
= 1 group - 1 box + 1 u
= 980 - 490 + 735
= 1225
Answer(s): 1225