Sarah and Penelope have some marbles. If Sarah gives 14 marbles to Penelope, Penelope will have 4 times the number of marbles as Sarah. If Penelope gives 24 marbles to Sarah, Sarah will have
12 as many marbles as Penelope. How many marbles does Sarah have at first?
|
Case 1 |
Case 2 |
|
Sarah |
Penelope |
Sarah |
Penelope |
Before |
3 u + 14 |
12 u - 14 |
5 u - 24 |
10 u + 24 |
Change |
- 14 |
+ 14 |
+ 24 |
- 24 |
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 Sarah had at first is the same in both cases.
5 u - 24 = 3 u + 14
5 u - 3 u = 14 + 24
2 u = 38
1 u = 19
Number of marbles that Sarah had at first
= 3 u + 14
= 3 x 19 + 14
= 57 + 14
= 71
Answer(s): 71