Three girls, Nicole, Zoe and Lynn had a total of 5400 marbles. Some exchanges were made. First, Nicole gave Zoe as many marbles as Zoe had. After that, Zoe gave
13 of whatever she had then to Lynn. Finally, Lynn gave
14 of whatever she had to Nicole. As a result, they each had the same number of marbles. How many marbles did Nicole have at first?
|
Nicole |
Zoe |
Lynn |
Total |
Before 1 |
? |
1 u |
|
5400 |
Change 1 |
- 1 u |
+ 1 u |
|
|
After 1 |
|
2 u |
|
|
Before 2 |
|
3 p |
|
5400 |
Change 2 |
|
- 1 p |
+ 1 p |
|
After 2 |
|
2 p |
|
|
Before 3 |
|
|
4 boxes |
5400 |
Change 3 |
+ 1 box |
|
- 1 box |
|
After 3 |
|
|
3 boxes |
|
After 3 |
1 group |
1 group |
1 group |
5400 |
3 groups = 5400
1 group = 5400 ÷ 3 = 1800
1 group = 3 boxes 3 boxes = 1800
1 box = 1800 ÷ 3 = 600
2 p = 1 group
1 p = 1800 ÷ 2 = 900
3 p = 3 x 900 = 2700
3 p = 2 u
2 u = 2700
1 u = 2700 ÷ 2 = 1350
Number of marbles that Nicole had at first
= 1 group - 1 box + 1 u
= 1800 - 600 + 1350
= 2550
Answer(s): 2550