Xuan and Dana have some coins. If Xuan gives 27 coins to Dana, Dana will have 3 times the number of coins as Xuan. If Dana gives 3 coins to Xuan, Xuan will have
23 as many coins as Dana. How many coins does Xuan have at first?
| |
Case 1 |
Case 2 |
| |
Xuan |
Dana |
Xuan |
Dana |
| Before |
5 u + 27 |
15 u - 27 |
8 u - 3 |
12 u + 3 |
| Change |
- 27 |
+ 27 |
+ 3 |
- 3 |
| 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 Xuan had at first is the same in both cases.
8 u - 3 = 5 u + 27
8 u - 5 u = 27 + 3
3 u = 30
1 u = 10
Number of coins that Xuan had at first
= 5 u + 27
= 5 x 10 + 27
= 50 + 27
= 77
Answer(s): 77
