Three girls, Esther, Gillian and Winnie had a total of 1500 marbles. Some exchanges were made. First, Esther gave Gillian as many marbles as Gillian had. After that, Gillian gave
13 of whatever she had then to Winnie. Finally, Winnie gave
15 of whatever she had to Esther. As a result, they each had the same number of marbles. How many marbles did Esther have at first?
|
Esther |
Gillian |
Winnie |
Total |
Before 1 |
? |
1 u |
|
1500 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1500 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
1500 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1500 |
3 groups = 1500
1 group = 1500 ÷ 3 = 500
1 group = 4 boxes 4 boxes = 500
1 box = 500 ÷ 4 = 125
2 p = 1 group
1 p = 500 ÷ 2 = 250
3 p = 3 x 250 = 750
3 p = 2 u
2 u = 750
1 u = 750 ÷ 2 = 375
Number of marbles that Esther had at first
= 1 group - 1 box + 1 u
= 500 - 125 + 375
= 750
Answer(s): 750