Pamela and Hazel have some coins. If Pamela gives 22 coins to Hazel, Hazel will have 4 times the number of coins as Pamela. If Hazel gives 18 coins to Pamela, Pamela will have
12 as many coins as Hazel. How many coins does Pamela have at first?
| |
Case 1 |
Case 2 |
| |
Pamela |
Hazel |
Pamela |
Hazel |
| Before |
3 u + 22 |
12 u - 22 |
5 u - 18 |
10 u + 18 |
| Change |
- 22 |
+ 22 |
+ 18 |
- 18 |
| After |
1x3 =
3 u |
4x3 =
12 u |
1x5 =
5 u |
2x5 =
10 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 5 and 3 is 15.
Number of coins that Pamela had at first is the same in both cases.
5 u - 18 = 3 u + 22
5 u - 3 u = 22 + 18
2 u = 40
1 u = 20
Number of coins that Pamela had at first
= 3 u + 22
= 3 x 20 + 22
= 60 + 22
= 82
Answer(s): 82
