SOLUTION: Immediate help! Answer all with solutio n and explanation. 1.When Ramon was 12 years old, his father was 40.How many years must past for Ramon to be 8 years older than one-f

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Immediate help! Answer all with solutio n and explanation. 1.When Ramon was 12 years old, his father was 40.How many years must past for Ramon to be 8 years older than one-f      Log On

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Question 929834: Immediate help! Answer all with solutio
n and explanation.
1.When Ramon was 12 years old, his father was
40.How many years must past for Ramon to be 8 years
older than one-fourth as old as his father.
2.The sum of the ages of Bobby and Mercy is 60. Nine
yrs ago Bobby was twice as old as Mercy was then.Find
their present age.
3.Tom is 8 yrs old than Steve. Three yrs ago Steve was
2 yrs more than one-third as old as Tom was then.
How old is Tom now?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.When Ramon was 12 years old, his father was
40.How many years must past for Ramon to be 8 years
older than one-fourth as old as his father.
let Ramon’s age x and father’s age y
let years be n


This is the overall picture
Who-----Now---Future
Ramon---12----x
Father---40---y


So, y-x=40-12=>y-x=28......eq.1
You can get your second equation from the data.
How many years must past for Ramon to be 8 years
older than one-fourth as old as his father.
12%2Bn=%281%2F4%29%2840%2Bn%29%2B8...........eq.2
Solve 12%2Bn=%281%2F4%29%2840%2Bn%29%2B8
12%2Bn=10%2Bn%2F4%2B8
n-n%2F4=10%2B8-12
3n%2F4=6
3n=24
n=8
check:
in 8 years Ramon will be 12%2B8=20 and his father 40%2B8=48
20=%281%2F4%2948%2B8
20=12%2B8
20=20
2.The sum of the ages of Bobby and Mercy is 60. Nine
yrs ago Bobby was twice as old as Mercy was then.Find
their present age.
let the ages of Bobby be B and Mercy M
given:
B%2BM=60 ...eq.1
Nine years ago Bobby was B twice as old as Mercy Mwas then.
2%28B-9%29=M-9........eq.2
solve the system:
B%2BM=60 ...eq.1
2%28B-9%29=M-9........eq.2
______________________________
B%2BM=60 ...eq.1 solve for B
B=60-M ...plug in eq.2
2%2860-M-9%29=M-9........eq.2...solve for M
120-2M-18=M-9
120-18%2B9=2M%2BM
111=3M
111%2F3=M
M=37
now find B
B=60-M
B=60-37
B=23


3.Tom is 8 yrs older than Steve. Three yrs ago Steve was
2 yrs more than one-third as old as Tom was then.
How old is Tom now?
T=S%2B8 ...eq.1
%281%2F3%29%28T-3%29=S-3........eq.2
_________________________________substitute T from eq.1 in eq.2
%281%2F3%29%28S%2B8-3%29=S-3........eq.2.........solve for S
%28S%2B8-3%29=%28S-3%293
S%2B5=3S-9
9%2B5=3S-S
14=2S
S=7
go to T=S%2B8 ...eq.1 .......solve for T
T=7%2B8
T=15