Three girls, Gem, Sarah and Roshel had a total of 4140 pens. Some exchanges were made. First, Gem gave Sarah as many pens as Sarah had. After that, Sarah gave
13 of whatever she had then to Roshel. Finally, Roshel gave
14 of whatever she had to Gem. As a result, they each had the same number of pens. How many pens did Gem have at first?
|
Gem |
Sarah |
Roshel |
Total |
Before 1 |
? |
1 u |
|
4140 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
4140 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
4140 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4140 |
3 groups = 4140
1 group = 4140 ÷ 3 = 1380
1 group = 3 boxes 3 boxes = 1380
1 box = 1380 ÷ 3 = 460
2 p = 1 group
1 p = 1380 ÷ 2 = 690
3 p = 3 x 690 = 2070
3 p = 2 u
2 u = 2070
1 u = 2070 ÷ 2 = 1035
Number of pens that Gem had at first
= 1 group - 1 box + 1 u
= 1380 - 460 + 1035
= 1955
Answer(s): 1955