Three girls, Victoria, Yoko and Xuan had a total of 1920 marbles. Some exchanges were made. First, Victoria gave Yoko as many marbles as Yoko had. After that, Yoko gave
13 of whatever she had then to Xuan. Finally, Xuan gave
13 of whatever she had to Victoria. As a result, they each had the same number of marbles. How many marbles did Victoria have at first?
|
Victoria |
Yoko |
Xuan |
Total |
Before 1 |
? |
1 u |
|
1920 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1920 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
1920 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1920 |
3 groups = 1920
1 group = 1920 ÷ 3 = 640
1 group = 2 boxes 2 boxes = 640
1 box = 640 ÷ 2 = 320
2 p = 1 group
1 p = 640 ÷ 2 = 320
3 p = 3 x 320 = 960
3 p = 2 u
2 u = 960
1 u = 960 ÷ 2 = 480
Number of marbles that Victoria had at first
= 1 group - 1 box + 1 u
= 640 - 320 + 480
= 800
Answer(s): 800