SOLUTION: rema is older than ken. the difference of their ages is 12 and the sum of their ages is 50. find the age of each

Question 133204: rema is older than ken. the difference of their ages is 12 and the sum of their ages is 50. find the age of each
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

If "the difference of their ages is 12", then the first equation is . Also, if "the sum of their ages is 50", then the second equation is .

So let's solve this system by using substitution

Start with the given system of equations:

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

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

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Combine like terms on the left side

Add 12 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

So the two ages are 31 and 19
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