Three girls, Gabby, Emma and Erika had a total of 5520 buttons. Some exchanges were made. First, Gabby gave Emma as many buttons as Emma had. After that, Emma gave
13 of whatever she had then to Erika. Finally, Erika gave
13 of whatever she had to Gabby. As a result, they each had the same number of buttons. How many buttons did Gabby have at first?
|
Gabby |
Emma |
Erika |
Total |
Before 1 |
? |
1 u |
|
5520 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5520 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
3 boxes |
5520 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5520 |
3 groups = 5520
1 group = 5520 ÷ 3 = 1840
1 group = 2 boxes 2 boxes = 1840
1 box = 1840 ÷ 2 = 920
2 p = 1 group
1 p = 1840 ÷ 2 = 920
3 p = 3 x 920 = 2760
3 p = 2 u
2 u = 2760
1 u = 2760 ÷ 2 = 1380
Number of buttons that Gabby had at first
= 1 group - 1 box + 1 u
= 1840 - 920 + 1380
= 2300
Answer(s): 2300