SOLUTION: There are 5 people standing in a room. Rick is 5 times the age of Mike who is half the age of Larry. Ed is 30 years younger than double Larry and Mike's combined ages. Daniel is 79

Question 255433: There are 5 people standing in a room. Rick is 5 times the age of Mike who is half the age of Larry. Ed is 30 years younger than double Larry and Mike's combined ages. Daniel is 79 years younger than Rick. The sum of their ages is 271. How old is Daniel?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
There are 5 people standing in a room.
:
Write an equation for each phrase; put everything in terms of m
:
Rick is 5 times the age of Mike;
R = 5M
:
who is half the age of Larry.
M = .5L
or
L = 2M
:
Ed is 30 years younger than double Larry and Mike's combined ages.
E = 2(L+M) - 30
E = 2L + 2M - 30
Replace L with 2M
E = 2(2M) + 2M - 30
E = 4M + 2M - 30
E = 6M - 30
:
Daniel is 79 years younger than Rick.
D = R - 79
Replace R with 5M
D = 5M - 79
:
the sum of their ages is 271.
R + M + L + E + D = 271
Find M
5M + M + 2M + (6M-30) + (5M-79) = 271
19M - 109 = 271
19M = 271 + 109
19M = 380
M =
M = 20
:
How old is Daniel?
D = 5M - 79
D = 5(20) - 79
D = 100 - 79
D = 21 yrs
;
:
Check solution by finding the age of each and totaling it
R = 5(20) = 100
L = 2(20) = 40
E = 6(20) - 30 = 90
:
R + M + L + E + D = 271
100 + 20 + 40 + 90 + 21 = 271
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