SOLUTION: Rodney and Rex are father and son, the sum of their age is 50. Five years ago Rodney was three times older than Rex, what are the linear equations to solve?

Question 127481: Rodney and Rex are father and son, the sum of their age is 50. Five years ago Rodney was three times older than Rex, what are the linear equations to solve?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let X equal Rodney's age and Y equal Rex's age.
.
The problem tells you that today the sum of their ages is 50. So we can write this in equation
form as:
.
X + Y = 50 <=== this is linear equation #1
.
Five years ago, how old was each? Rodney would have been (X - 5) and Rex would have been (Y - 5)
.
At that time Rodney was 3 times as old as Rex. That means their ages would have been equal
if you multiplied Rex's age by 3. In equation form this would be:
.
X - 5 = 3(Y - 5)
.
Multiply out the right side of this equation and you have:
.
X - 5 = 3Y - 15
.
Get rid of the -5 on the left side by adding 5 to both sides to get:
.
X = 3Y - 10
.
Get rid of the 3Y on the right side by subtracting 3Y from both sides and you have:
.
X - 3Y = -10 <=== this is linear equation #2
.
So the set of equations to solve consists of the two equations:
.
X + Y = +50 and
X -3Y = -10
.
Subtracting these two equations in their vertical columns eliminates the terms involving X
and results in:
.
4Y = 60
.
Solve for Y by dividing both sides of this equation by 4 to get:
.
Y = 60/4 = 15
.
Y was Rex's age so Rex is the son. Since the Father is Rodney, then he has to be 35 years old
because the sum of his age and Rex's age must be 50.
.
Five years ago Rex would have been 10 years old at the time. And 5 years ago Rodney would
have been 30. So Rodney's age would have been 3 times Rex's age, just as the problem said
it should be.
.
Hope this helps you to understand the problem and how to set up and solve the equations.
.

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