Question 1166098
The site has so many of these.  Students should be able to find a gigantic number of them already solved.




---------


=================================================================================================================================
PersonOne is n years younger than personTwo.  p years ago, personTwo's age was k times personOnes age.  How old is each person now?
===================================================================================================================================


x, age of personOne
y, age of personTwo


{{{system(x=y-n,y-p=k(x-p))}}}


Substituting x from first equation into the second equation
{{{y-p=k(y-n-p)}}}
{{{y-p=ky-kn-kp}}}
{{{ky-kn-kp=y-p}}}
{{{ky-y=-p+kn+kp}}}
{{{y(k-1)=kn+kp-p}}}
{{{highlight(y=(kn+kp-p)/(k-1))}}}-----------personTwo's age


Now to FIND for x
Use {{{y=x+n}}}; substitute.
{{{x+n-p=k(x-p)}}}
{{{x+n-p=kx-kp}}}
{{{n-p=kx-kp-x}}}
{{{n-p+kp=kx-x}}}
{{{n-p+kp=(k-1)x}}}
{{{highlight(x=(n-p+kp)/(k-1))}}}------------personOne's age