David, Nick and Carl have some marbles. The ratios of their marbles are as follows:
David : (David + Nick + Carl) = 3 : 7
Nick : (David + Carl) = 1 : 3
Carl has 10 marbles more than Nick. In the end, Carl gives away all he has to Nick and David so that both Nick and David end up with the same number of marbles, how many marbles has Nick received from Carl?
Nick |
Carl |
David |
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 Carl has more than Nick
= 9 u - 7 u
= 2 u
2 u = 10
1 u = 10 ÷ 2 = 5
|
Nick |
Carl |
David |
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 Nick has received from Carl
= 14 u - 7 u
= 7 u
= 7 x 5
= 35
Answer(s): 35