David, Ben and Warren have some marbles. The ratios of their marbles are as follows:
David : (David + Ben + Warren) = 3 : 7
Ben : (David + Warren) = 1 : 5
Warren has 30 marbles more than Ben. In the end, Warren gives away all he has to Ben and David so that both Ben and David end up with the same number of marbles, how many marbles has David received from Warren?
Ben |
Warren |
David |
Total |
4x6 |
3x6 |
7x6 |
1x7 |
5x7 |
6x7 |
7 u |
17 u |
18 u |
42 u |
The total number of marbles is repeated. Make the total number of marbles the same. LCM of 7 and 6 is 42.
Number of marbles that Warren has more than Ben
= 17 u - 7 u
= 10 u
10 u = 30
1 u = 30 ÷ 10 = 3
|
Ben |
Warren |
David |
Before |
7 u |
17 u |
18 u |
Change |
+ 14 u |
- 17 u |
+ 3 u |
After |
21 u |
0 u |
21 u |
Number of marbles that David has received from Warren
= 21 u - 18 u
= 3 u
= 3 x 3
= 9
Answer(s): 9