Three girls, Gabby, Jen and Roshel had a total of 3720 marbles. Some exchanges were made. First, Gabby gave Jen as many marbles as Jen had. After that, Jen gave
13 of whatever she had then to Roshel. Finally, Roshel gave
13 of whatever she had to Gabby. As a result, they each had the same number of marbles. How many marbles did Gabby have at first?
|
Gabby |
Jen |
Roshel |
Total |
Before 1 |
? |
1 u |
|
3720 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
3720 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
3720 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
3720 |
3 groups = 3720
1 group = 3720 ÷ 3 = 1240
1 group = 2 boxes 2 boxes = 1240
1 box = 1240 ÷ 2 = 620
2 p = 1 group
1 p = 1240 ÷ 2 = 620
3 p = 3 x 620 = 1860
3 p = 2 u
2 u = 1860
1 u = 1860 ÷ 2 = 930
Number of marbles that Gabby had at first
= 1 group - 1 box + 1 u
= 1240 - 620 + 930
= 1550
Answer(s): 1550