Olivia and Kimberly have some marbles. If Olivia gives 31 marbles to Kimberly, Kimberly will have 5 times the number of marbles as Olivia. If Kimberly gives 60 marbles to Olivia, Olivia will have
23 as many marbles as Kimberly. How many marbles does Olivia have at first?
|
Case 1 |
Case 2 |
|
Olivia |
Kimberly |
Olivia |
Kimberly |
Before |
5 u + 31 |
25 u - 31 |
12 u - 60 |
18 u + 60 |
Change |
- 31 |
+ 31 |
+ 60 |
- 60 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 6 and 5 is 30.
Number of marbles that Olivia had at first is the same in both cases.
12 u - 60 = 5 u + 31
12 u - 5 u = 31 + 60
7 u = 91
1 u = 13
Number of marbles that Olivia had at first
= 5 u + 31
= 5 x 13 + 31
= 65 + 31
= 96
Answer(s): 96