Luke, Oliver and Billy have some cards. The ratios of their cards are as follows:
Luke : (Luke + Oliver + Billy) = 1 : 5
Oliver : (Luke + Billy) = 1 : 5
Billy has 56 cards more than Oliver. In the end, Billy gives away all he has to Oliver and Luke so that both Oliver and Luke end up with the same number of cards, how many cards has Oliver received from Billy?
Oliver |
Billy |
Luke |
Total |
4x6 |
1x6 |
5x6 |
1x5 |
5x5 |
6x5 |
5 u |
19 u |
6 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 Oliver
= 19 u - 5 u
= 14 u
14 u = 56
1 u = 56 ÷ 14 = 4
|
Oliver |
Billy |
Luke |
Before |
5 u |
19 u |
6 u |
Change |
+ 10 u |
- 19 u |
+ 9 u |
After |
15 u |
0 u |
15 u |
Number of cards that Oliver has received from Billy
= 15 u - 5 u
= 10 u
= 10 x 4
= 40
Answer(s): 40