Three girls, Zara, Raeann and Gem had a total of 5580 pens. Some exchanges were made. First, Zara gave Raeann as many pens as Raeann had. After that, Raeann gave
13 of whatever she had then to Gem. Finally, Gem gave
14 of whatever she had to Zara. As a result, they each had the same number of pens. How many pens did Zara have at first?
|
Zara |
Raeann |
Gem |
Total |
Before 1 |
? |
1 u |
|
5580 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5580 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
5580 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5580 |
3 groups = 5580
1 group = 5580 ÷ 3 = 1860
1 group = 3 boxes 3 boxes = 1860
1 box = 1860 ÷ 3 = 620
2 p = 1 group
1 p = 1860 ÷ 2 = 930
3 p = 3 x 930 = 2790
3 p = 2 u
2 u = 2790
1 u = 2790 ÷ 2 = 1395
Number of pens that Zara had at first
= 1 group - 1 box + 1 u
= 1860 - 620 + 1395
= 2635
Answer(s): 2635