Three girls, Gabby, Hilda and Tiffany had a total of 5400 marbles. Some exchanges were made. First, Gabby gave Hilda as many marbles as Hilda had. After that, Hilda gave
15 of whatever she had then to Tiffany. Finally, Tiffany 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 |
Hilda |
Tiffany |
Total |
Before 1 |
? |
1 u |
|
5400 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
5400 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
3 boxes |
5400 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5400 |
3 groups = 5400
1 group = 5400 ÷ 3 = 1800
1 group = 2 boxes 2 boxes = 1800
1 box = 1800 ÷ 2 = 900
4 p = 1 group
1 p = 1800 ÷ 4 = 450
5 p = 5 x 450 = 2250
5 p = 2 u
2 u = 2250
1 u = 2250 ÷ 2 = 1125
Number of marbles that Gabby had at first
= 1 group - 1 box + 1 u
= 1800 - 900 + 1125
= 2025
Answer(s): 2025