Three girls, Wendy, Xuan and Cathy had a total of 840 marbles. Some exchanges were made. First, Wendy gave Xuan as many marbles as Xuan had. After that, Xuan gave
15 of whatever she had then to Cathy. Finally, Cathy gave
13 of whatever she had to Wendy. As a result, they each had the same number of marbles. How many marbles did Wendy have at first?
|
Wendy |
Xuan |
Cathy |
Total |
Before 1 |
? |
1 u |
|
840 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
5 p |
|
840 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
4 p |
|
|
Before 3 |
|
|
3 boxes |
840 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
840 |
3 groups = 840
1 group = 840 ÷ 3 = 280
1 group = 2 boxes 2 boxes = 280
1 box = 280 ÷ 2 = 140
4 p = 1 group
1 p = 280 ÷ 4 = 70
5 p = 5 x 70 = 350
5 p = 2 u
2 u = 350
1 u = 350 ÷ 2 = 175
Number of marbles that Wendy had at first
= 1 group - 1 box + 1 u
= 280 - 140 + 175
= 315
Answer(s): 315