Question 132068
Joe is x years old
Mary is y years old
We are given that {{{x+y=60}}}


Ten years ago, Joe was x - 10 years old and Mary was y - 10 years old.
We are given that {{{x-10=3(y-10)}}}


Put the second relationship into standard form ({{{ax+by=c}}})
{{{x-10=3(y-10)}}}
{{{x-10=3y-30}}}
{{{x-3y=-30+10}}}
{{{x-3y=-20}}}


Now we have two equations in standard form:
{{{x+y=60}}}
{{{x-3y=-20}}}


Multiply the second equation by -1:
{{{-x+3y=20}}}


Add the first equation to the second, term by term:
{{{0x+4y=80}}}


Divide by the coefficient on y:
{{{y=20}}}


Therefore Mary is 20 years old now.  That means that Joe is 40 years old now (60 - 20).  Ten years ago, Joe would have been 30 and Mary would have been 10, and 30 is 3 times 10.  Answer checks.