Three girls, Hilda, Irene and Esther had a total of 1800 coins. Some exchanges were made. First, Hilda gave Irene as many coins as Irene had. After that, Irene gave
13 of whatever she had then to Esther. Finally, Esther gave
15 of whatever she had to Hilda. As a result, they each had the same number of coins. How many coins did Hilda have at first?
|
Hilda |
Irene |
Esther |
Total |
Before 1 |
? |
1 u |
|
1800 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
1800 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 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
2 p = 1 group
1 p = 600 ÷ 2 = 300
3 p = 3 x 300 = 900
3 p = 2 u
2 u = 900
1 u = 900 ÷ 2 = 450
Number of coins that Hilda had at first
= 1 group - 1 box + 1 u
= 600 - 150 + 450
= 900
Answer(s): 900