Three girls, Gwen, Xuan and Diana had a total of 2280 pens. Some exchanges were made. First, Gwen gave Xuan as many pens as Xuan had. After that, Xuan gave
13 of whatever she had then to Diana. Finally, Diana gave
15 of whatever she had to Gwen. As a result, they each had the same number of pens. How many pens did Gwen have at first?
|
Gwen |
Xuan |
Diana |
Total |
Before 1 |
? |
1 u |
|
2280 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
2280 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
2280 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2280 |
3 groups = 2280
1 group = 2280 ÷ 3 = 760
1 group = 4 boxes 4 boxes = 760
1 box = 760 ÷ 4 = 190
2 p = 1 group
1 p = 760 ÷ 2 = 380
3 p = 3 x 380 = 1140
3 p = 2 u
2 u = 1140
1 u = 1140 ÷ 2 = 570
Number of pens that Gwen had at first
= 1 group - 1 box + 1 u
= 760 - 190 + 570
= 1140
Answer(s): 1140