Linda and Sarah have some coins. If Linda gives 12 coins to Sarah, Sarah will have 3 times the number of coins as Linda. If Sarah gives 15 coins to Linda, Linda will have
23 as many coins as Sarah. How many coins does Linda have at first?
| |
Case 1 |
Case 2 |
| |
Linda |
Sarah |
Linda |
Sarah |
| Before |
5 u + 12 |
15 u - 12 |
8 u - 15 |
12 u + 15 |
| Change |
- 12 |
+ 12 |
+ 15 |
- 15 |
| After |
1x5 =
5 u |
3x5 =
15 u |
2x4 =
8 u |
3x4 =
12 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 4 and 5 is 20.
Number of coins that Linda had at first is the same in both cases.
8 u - 15 = 5 u + 12
8 u - 5 u = 12 + 15
3 u = 27
1 u = 9
Number of coins that Linda had at first
= 5 u + 12
= 5 x 9 + 12
= 45 + 12
= 57
Answer(s): 57
