Three girls, Zoe, Abi and Xylia had a total of 2520 buttons. Some exchanges were made. First, Zoe gave Abi as many buttons as Abi had. After that, Abi gave
14 of whatever she had then to Xylia. Finally, Xylia gave
13 of whatever she had to Zoe. As a result, they each had the same number of buttons. How many buttons did Zoe have at first?
|
Zoe |
Abi |
Xylia |
Total |
Before 1 |
? |
1 u |
|
2520 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
4 p |
|
2520 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
3 p |
|
|
Before 3 |
|
|
3 boxes |
2520 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
2 boxes |
|
After 3 |
1 group |
1 group |
1 group |
2520 |
3 groups = 2520
1 group = 2520 ÷ 3 = 840
1 group = 2 boxes 2 boxes = 840
1 box = 840 ÷ 2 = 420
3 p = 1 group
1 p = 840 ÷ 3 = 280
4 p = 4 x 280 = 1120
4 p = 2 u
2 u = 1120
1 u = 1120 ÷ 2 = 560
Number of buttons that Zoe had at first
= 1 group - 1 box + 1 u
= 840 - 420 + 560
= 980
Answer(s): 980