SOLUTION: Hi! I have a college algebra problem that says: Three years from now a man will be three times as old as his son will be. Two years ago he was four times as old as his son wa

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Question 1127049: Hi!
I have a college algebra problem that says:
Three years from now a man will be three times as old as his son will be. Two years ago he was four times as old as his son was. How old are they now?
Would the equation be 3x+3=2-4x
Thank you
-Maddie
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


The man's age now =
His son's age now =
Three years from now:
a man will be:
his son will be:
since three years from now a man will be three times as old as his son will be, we have
...solve or

............eq.1

Two years ago:



if he was four times as old as his son was,we have
...solve or

...........eq.2
from eq.1 and eq.2 we have
....solve or


find
...........eq.2


The man's age now =
His son's age now =


Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

            A canonical way to solve this problem is to start with two unknowns. 


Let x be the son's age now;  let y be the man's age now.



Then in three years

y+3 = 3*(x+3).     (1)


It is your first equation.  The second equation is


y-2 = 4*(x-2).     (2)     <<<---===  It describes what happened 2 years ago . . . 



To solve this system of equation, I will apply the Substitution method.

From equation (1), I express  y = 3*(x+3) - 3  and substitute it into equation (2). Then I get a single equation for only one unknown x,

which is easy to solve :


(3*(x+3) -3) - 2 = 4*(x-2).


Simplify and solve it step by step


3x + 9 - 3 - 2 = 4x - 8

9 - 3 + 8 - 2 = 4x - 3x

12 = x.


Answer.  The son is 12 years old.  The man is  y = 3*(x+3)-3 = 3*(12+3) - 3 = 3*15 - 3 = 42 years old.

Solved.

Please check my answer on your own.

---------------

Maddie, if you have difficulties in understanding and solving age word problems, then you may find useful for you
to look into the collection of my lessons on this subject in this site.

They are
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problem
    - Selected age word problems from the archive
    - Age problems for mental solution

Read them and become an expert in solving age problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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