Usha and Olivia have some coins. If Usha gives 26 coins to Olivia, Olivia will have 4 times the number of coins as Usha. If Olivia gives 6 coins to Usha, Usha will have
12 as many coins as Olivia. How many coins does Usha have at first?
|
Case 1 |
Case 2 |
|
Usha |
Olivia |
Usha |
Olivia |
Before |
3 u + 26 |
12 u - 26 |
5 u - 6 |
10 u + 6 |
Change |
- 26 |
+ 26 |
+ 6 |
- 6 |
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 Usha had at first is the same in both cases.
5 u - 6 = 3 u + 26
5 u - 3 u = 26 + 6
2 u = 32
1 u = 16
Number of coins that Usha had at first
= 3 u + 26
= 3 x 16 + 26
= 48 + 26
= 74
Answer(s): 74