Three girls, Xylia, Emily and Diana had a total of 1140 marbles. Some exchanges were made. First, Xylia gave Emily as many marbles as Emily had. After that, Emily gave
13 of whatever she had then to Diana. Finally, Diana gave
15 of whatever she had to Xylia. As a result, they each had the same number of marbles. How many marbles did Xylia have at first?
|
Xylia |
Emily |
Diana |
Total |
Before 1 |
? |
1 u |
|
1140 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1140 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
1140 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
1140 |
3 groups = 1140
1 group = 1140 ÷ 3 = 380
1 group = 4 boxes 4 boxes = 380
1 box = 380 ÷ 4 = 95
2 p = 1 group
1 p = 380 ÷ 2 = 190
3 p = 3 x 190 = 570
3 p = 2 u
2 u = 570
1 u = 570 ÷ 2 = 285
Number of marbles that Xylia had at first
= 1 group - 1 box + 1 u
= 380 - 95 + 285
= 570
Answer(s): 570