Cindy and Yen have some coins. If Cindy gives 30 coins to Yen, Yen will have 3 times the number of coins as Cindy. If Yen gives 6 coins to Cindy, Cindy will have
23 as many coins as Yen. How many coins does Cindy have at first?
| |
Case 1 |
Case 2 |
| |
Cindy |
Yen |
Cindy |
Yen |
| Before |
5 u + 30 |
15 u - 30 |
8 u - 6 |
12 u + 6 |
| Change |
- 30 |
+ 30 |
+ 6 |
- 6 |
| 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 Cindy had at first is the same in both cases.
8 u - 6 = 5 u + 30
8 u - 5 u = 30 + 6
3 u = 36
1 u = 12
Number of coins that Cindy had at first
= 5 u + 30
= 5 x 12 + 30
= 60 + 30
= 90
Answer(s): 90
