Three girls, Irene, Hilda and Opal had a total of 2040 marbles. Some exchanges were made. First, Irene gave Hilda as many marbles as Hilda had. After that, Hilda gave
13 of whatever she had then to Opal. Finally, Opal gave
15 of whatever she had to Irene. As a result, they each had the same number of marbles. How many marbles did Irene have at first?
|
Irene |
Hilda |
Opal |
Total |
Before 1 |
? |
1 u |
|
2040 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
2040 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
5 boxes |
2040 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
4 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2040 |
3 groups = 2040
1 group = 2040 ÷ 3 = 680
1 group = 4 boxes 4 boxes = 680
1 box = 680 ÷ 4 = 170
2 p = 1 group
1 p = 680 ÷ 2 = 340
3 p = 3 x 340 = 1020
3 p = 2 u
2 u = 1020
1 u = 1020 ÷ 2 = 510
Number of marbles that Irene had at first
= 1 group - 1 box + 1 u
= 680 - 170 + 510
= 1020
Answer(s): 1020