Victoria and Xandra have some coins. If Victoria gives 23 coins to Xandra, Xandra will have 4 times the number of coins as Victoria. If Xandra gives 61 coins to Victoria, Victoria will have
35 as many coins as Xandra. How many coins does Victoria have at first?
|
Case 1 |
Case 2 |
|
Victoria |
Xandra |
Victoria |
Xandra |
Before |
8 u + 23 |
32 u - 23 |
15 u - 61 |
25 u + 61 |
Change |
- 23 |
+ 23 |
+ 61 |
- 61 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 u |
5x5 = 25 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 8 is 40.
Number of coins that Victoria had at first is the same in both cases.
15 u - 61 = 8 u + 23
15 u - 8 u = 23 + 61
7 u = 84
1 u = 12
Number of coins that Victoria had at first
= 8 u + 23
= 8 x 12 + 23
= 96 + 23
= 119
Answer(s): 119