Billy, Valen and David have some marbles. The ratios of their marbles are as follows:
Billy : (Billy + Valen + David) = 3 : 7
Valen : (Billy + David) = 1 : 3
David has 4 marbles more than Valen. In the end, David gives away all he has to Valen and Billy so that both Valen and Billy end up with the same number of marbles, how many marbles has Billy received from David?
Valen |
David |
Billy |
Total |
4x4 |
3x4 |
7x4 |
1x7 |
3x7 |
4x7 |
7 u |
9 u |
12 u |
28 u |
The total number of marbles is repeated. Make the total number of marbles the same. LCM of 7 and 4 is 28.
Number of marbles that David has more than Valen
= 9 u - 7 u
= 2 u
2 u = 4
1 u = 4 ÷ 2 = 2
|
Valen |
David |
Billy |
Before |
7 u |
9 u |
12 u |
Change |
+ 7 u |
- 9 u |
+ 2 u |
After |
14 u |
0 u |
14 u |
Number of marbles that Billy has received from David
= 14 u - 12 u
= 2 u
= 2 x 2
= 4
Answer(s): 4