Julian, Caden and Billy have some cards. The ratios of their cards are as follows:
Julian : (Julian + Caden + Billy) = 2 : 5
Caden : (Julian + Billy) = 1 : 5
Billy has 96 cards more than Caden. In the end, Billy gives away all he has to Caden and Julian so that both Caden and Julian end up with the same number of cards, how many cards has Caden received from Billy?
Caden |
Billy |
Julian |
Total |
3x6 |
2x6 |
5x6 |
1x5 |
5x5 |
6x5 |
5 u |
13 u |
12 u |
30 u |
The total number of cards is repeated. Make the total number of cards the same. LCM of 5 and 6 is 30.
Number of cards that Billy has more than Caden
= 13 u - 5 u
= 8 u
8 u = 96
1 u = 96 ÷ 8 = 12
|
Caden |
Billy |
Julian |
Before |
5 u |
13 u |
12 u |
Change |
+ 10 u |
- 13 u |
+ 3 u |
After |
15 u |
0 u |
15 u |
Number of cards that Caden has received from Billy
= 15 u - 5 u
= 10 u
= 10 x 12
= 120
Answer(s): 120