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

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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