Valen, Xavier and Ivan have some cards. The ratios of their cards are as follows:
Valen : (Valen + Xavier + Ivan) = 1 : 3
Xavier : (Valen + Ivan) = 1 : 3
Ivan has 22 cards more than Xavier. In the end, Ivan gives away all he has to Xavier and Valen so that both Xavier and Valen end up with the same number of cards, how many cards has Xavier received from Ivan?
Xavier |
Ivan |
Valen |
Total |
2x4 |
1x4 |
3x4 |
1x3 |
3x3 |
4x3 |
3 u |
5 u |
4 u |
12 u |
The total number of cards is repeated. Make the total number of cards the same. LCM of 3 and 4 is 12.
Number of cards that Ivan has more than Xavier
= 5 u - 3 u
= 2 u
2 u = 22
1 u = 22 ÷ 2 = 11
|
Xavier |
Ivan |
Valen |
Before |
3 u |
5 u |
4 u |
Change |
+ 3 u |
- 5 u |
+ 2 u |
After |
6 u |
0 u |
6 u |
Number of cards that Xavier has received from Ivan
= 6 u - 3 u
= 3 u
= 3 x 11
= 33
Answer(s): 33