Three girls, Olivia, Tiffany and Shannon had a total of 4140 pens. Some exchanges were made. First, Olivia gave Tiffany as many pens as Tiffany had. After that, Tiffany gave
14 of whatever she had then to Shannon. Finally, Shannon gave
13 of whatever she had to Olivia. As a result, they each had the same number of pens. How many pens did Olivia have at first?
|
Olivia |
Tiffany |
Shannon |
Total |
Before 1 |
? |
1 u |
|
4140 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
4140 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
3 boxes |
4140 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
4140 |
3 groups = 4140
1 group = 4140 ÷ 3 = 1380
1 group = 2 boxes 2 boxes = 1380
1 box = 1380 ÷ 2 = 690
3 p = 1 group
1 p = 1380 ÷ 3 = 460
4 p = 4 x 460 = 1840
4 p = 2 u
2 u = 1840
1 u = 1840 ÷ 2 = 920
Number of pens that Olivia had at first
= 1 group - 1 box + 1 u
= 1380 - 690 + 920
= 1610
Answer(s): 1610