Nicole and Anna have some marbles. If Nicole gives 26 marbles to Anna, Anna will have 4 times the number of marbles as Nicole. If Anna gives 14 marbles to Nicole, Nicole will have
12 as many marbles as Anna. How many marbles does Nicole have at first?
| |
Case 1 |
Case 2 |
| |
Nicole |
Anna |
Nicole |
Anna |
| Before |
3 u + 26 |
12 u - 26 |
5 u - 14 |
10 u + 14 |
| Change |
- 26 |
+ 26 |
+ 14 |
- 14 |
| After |
1x3 =
3 u |
4x3 =
12 u |
1x5 =
5 u |
2x5 =
10 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 5 and 3 is 15.
Number of marbles that Nicole had at first is the same in both cases.
5 u - 14 = 3 u + 26
5 u - 3 u = 26 + 14
2 u = 40
1 u = 20
Number of marbles that Nicole had at first
= 3 u + 26
= 3 x 20 + 26
= 60 + 26
= 86
Answer(s): 86
