Three girls, Olivia, Usha and Esther had a total of 2880 marbles. Some exchanges were made. First, Olivia gave Usha as many marbles as Usha had. After that, Usha gave
15 of whatever she had then to Esther. Finally, Esther gave
13 of whatever she had to Olivia. As a result, they each had the same number of marbles. How many marbles did Olivia have at first?
|
Olivia |
Usha |
Esther |
Total |
Before 1 |
? |
1 u |
|
2880 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
2880 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
3 boxes |
2880 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2880 |
3 groups = 2880
1 group = 2880 ÷ 3 = 960
1 group = 2 boxes 2 boxes = 960
1 box = 960 ÷ 2 = 480
4 p = 1 group
1 p = 960 ÷ 4 = 240
5 p = 5 x 240 = 1200
5 p = 2 u
2 u = 1200
1 u = 1200 ÷ 2 = 600
Number of marbles that Olivia had at first
= 1 group - 1 box + 1 u
= 960 - 480 + 600
= 1080
Answer(s): 1080