Three girls, Raeann, Gem and Julie had a total of 1800 marbles. Some exchanges were made. First, Raeann gave Gem as many marbles as Gem had. After that, Gem gave
15 of whatever she had then to Julie. Finally, Julie gave
15 of whatever she had to Raeann. As a result, they each had the same number of marbles. How many marbles did Raeann have at first?
|
Raeann |
Gem |
Julie |
Total |
Before 1 |
? |
1 u |
|
1800 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
1800 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
5 boxes |
1800 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1800 |
3 groups = 1800
1 group = 1800 ÷ 3 = 600
1 group = 4 boxes 4 boxes = 600
1 box = 600 ÷ 4 = 150
4 p = 1 group
1 p = 600 ÷ 4 = 150
5 p = 5 x 150 = 750
5 p = 2 u
2 u = 750
1 u = 750 ÷ 2 = 375
Number of marbles that Raeann had at first
= 1 group - 1 box + 1 u
= 600 - 150 + 375
= 825
Answer(s): 825