Pamela and Tammy have some marbles. If Pamela gives 29 marbles to Tammy, Tammy will have 3 times the number of marbles as Pamela. If Tammy gives 25 marbles to Pamela, Pamela will have
23 as many marbles as Tammy. How many marbles does Pamela have at first?
|
Case 1 |
Case 2 |
|
Pamela |
Tammy |
Pamela |
Tammy |
Before |
5 u + 29 |
15 u - 29 |
8 u - 25 |
12 u + 25 |
Change |
- 29 |
+ 29 |
+ 25 |
- 25 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 4 and 5 is 20.
Number of marbles that Pamela had at first is the same in both cases.
8 u - 25 = 5 u + 29
8 u - 5 u = 29 + 25
3 u = 54
1 u = 18
Number of marbles that Pamela had at first
= 5 u + 29
= 5 x 18 + 29
= 90 + 29
= 119
Answer(s): 119