SOLUTION: Rick is 5 times the age of Mike, who is half the age of Ed. Fred is double the ages of Mike and Ed combined. Daniel is 79 years younger than Rick. All thier ages equal 271. What i

Question 177817: Rick is 5 times the age of Mike, who is half the age of Ed. Fred is double the ages of Mike and Ed combined. Daniel is 79 years younger than Rick. All thier ages equal 271. What is the age of Daniel.
Found 3 solutions by stanbon, Mathtut, ptaylor:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Rick is 5 times the age of Mike, who is half the age of Ed. Fred is double the ages of Mike and Ed combined. Daniel is 79 years younger than Rick. All thier ages equal 271. What is the age of Daniel.
-------------------
R = 5M
M = (1/2)E
F = 2(M + E)
D = R-79
R + M + F + E + D = 271
---------------------------
Rearrange:
R + M + F + E + D = 271
R - 5M + 0 + 0 + 0 = 0
0 + 2M + 0 - E + 0 = 0
0 + 2M - F +2E + 0 = 0
R + 0 + 0 + 0 - D = 79
----------------------------
Solve the system by any method you know to get:
R =
M =
F =
E =
D =
----------
Comment:
This set of equations does not yield whole number values for the variables.
The equations are based on the words used in the narrative.
Check the words; make sure they express the problem you are trying to solve.
--------------------------------------------------
Cheers,
Stan H.

Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!

R + M + F + E + D = 271
R - 5M + 0 + 0 + 0 = 0
0 + 2M + 0 - E + 0 = 0
0 + 2M - F +2E + 0 = 0
R + 0 + 0 + 0 - D = 79
------------------------
:
Solving
:
R = 92.1
M = 18.42
F = 110.52
E = 36.84
D = 13.1

Answer by ptaylor(2198)   (Show Source): You can put this solution on YOUR website!

ANOTHER WAY
Let x=Ed's age
Then x/2 = Mike's age
And 5*(x/2)=Rick's age
And Fred's age =2((x/2) + x)=2*(3x/2)=6x/2=3x
Daniel's age=5*(x/2)-79
So:
x+(x/2)+5*(x/2)+3x +5(x/2)-79=271 simplify some
x+(x/2)+(5x/2)+3x+(5x/2)-79=271 add 79 to each side and simplify some more
(2x/2)+(x/2)+(5x/2)+(6x/2)+(5x/2)=271+79 collect like terms
(19x/2)=350 multiply each side by 2
19x=700 divide each side by 19
x=36.8
So, Daniel's age=5*(36.8/2)-79=184/2-79=92-79=13 years old
Hope this helps----ptaylor
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