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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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) About Me  (Show Source):
You can put this solution on YOUR website!


If "the difference of their ages is 12", then the first equation is x-y=12. Also, if "the sum of their ages is 50", then the second equation is x%2By=50.



So let's solve this system by using substitution







Start with the given system of equations:

system%28x-y=12%2Cx%2By=50%29



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

x-y=12 Start with the first equation


-y=12-x Subtract x from both sides


-y=-x%2B12 Rearrange the equation


y=%28-x%2B12%29%2F%28-1%29 Divide both sides by -1


y=%28%28-1%29%2F%28-1%29%29x%2B%2812%29%2F%28-1%29 Break up the fraction


y=x-12 Reduce



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

Since y=x-12, we can now replace each y in the second equation with x-12 to solve for x



x%2Bhighlight%28%28x-12%29%29=50 Plug in y=x-12 into the first equation. In other words, replace each y with x-12. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x-12=50 Combine like terms on the left side


2x=50%2B12Add 12 to both sides


2x=62 Combine like terms on the right side


x=%2862%29%2F%282%29 Divide both sides by 2 to isolate x



x=31 Divide





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


So the first part of our answer is: x=31









Since we know that x=31 we can plug it into the equation y=x-12 (remember we previously solved for y in the first equation).



y=x-12 Start with the equation where y was previously isolated.


y=%2831%29-12 Plug in x=31


y=31-12 Multiply


y=19 Combine like terms



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


So the second part of our answer is: y=19









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

So our answers are:

x=31 and y=19


So the two ages are 31 and 19