Three girls, Gwen, Natalie and Sabrina had a total of 5640 pens. Some exchanges were made. First, Gwen gave Natalie as many pens as Natalie had. After that, Natalie gave
13 of whatever she had then to Sabrina. Finally, Sabrina 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 |
Natalie |
Sabrina |
Total |
Before 1 |
? |
1 u |
|
5640 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5640 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
5640 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5640 |
3 groups = 5640
1 group = 5640 ÷ 3 = 1880
1 group = 4 boxes 4 boxes = 1880
1 box = 1880 ÷ 4 = 470
2 p = 1 group
1 p = 1880 ÷ 2 = 940
3 p = 3 x 940 = 2820
3 p = 2 u
2 u = 2820
1 u = 2820 ÷ 2 = 1410
Number of pens that Gwen had at first
= 1 group - 1 box + 1 u
= 1880 - 470 + 1410
= 2820
Answer(s): 2820