Anna and Hilda have some coins. If Anna gives 14 coins to Hilda, Hilda will have 5 times the number of coins as Anna. If Hilda gives 26 coins to Anna, Anna will have
35 as many coins as Hilda. How many coins does Anna have at first?
|
Case 1 |
Case 2 |
|
Anna |
Hilda |
Anna |
Hilda |
Before |
4 u + 14 |
20 u - 14 |
9 u - 26 |
15 u + 26 |
Change |
- 14 |
+ 14 |
+ 26 |
- 26 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 6 and 8 is 24.
Number of coins that Anna had at first is the same in both cases.
9 u - 26 = 4 u + 14
9 u - 4 u = 14 + 26
5 u = 40
1 u = 8
Number of coins that Anna had at first
= 4 u + 14
= 4 x 8 + 14
= 32 + 14
= 46
Answer(s): 46