Tim, Ethan and Daniel have some marbles. The ratios of their marbles are as follows:
Tim : (Tim + Ethan + Daniel) = 3 : 7
Ethan : (Tim + Daniel) = 1 : 3
Daniel has 24 marbles more than Ethan. In the end, Daniel gives away all he has to Ethan and Tim so that both Ethan and Tim end up with the same number of marbles, how many marbles has Tim received from Daniel?
Ethan |
Daniel |
Tim |
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 Daniel has more than Ethan
= 9 u - 7 u
= 2 u
2 u = 24
1 u = 24 ÷ 2 = 12
|
Ethan |
Daniel |
Tim |
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 Tim has received from Daniel
= 14 u - 12 u
= 2 u
= 2 x 12
= 24
Answer(s): 24