Question 113476
Let's say Mary is m years old, and Susan is s years old.  So twice Susan's age is 2s.  Ten years younger than that is 2s - 10.  Since that is Mary's age now, we can write:


{{{m = 2s - 10}}}


Five years from now, Mary will be m + 5 years old, and Susan will be s + 5 years old.  And the problem tells us that Mary will be eight years older than Susan then.  So we can also write:


{{{m + 5=s+5+8}}} or
{{{m+5=s+13}}}


Since we know that {{{m=2s-10}}} we can substitute this expression in the second equation.


{{{(2s-10)+5=s+13}}}


Now solve for s:
{{{2s-5=s+13}}}  Collect terms
{{{2s-s=13+5}}}  Add -s and +5 to both sides
{{{s=18}}}


So Susan is 18.  Let's put this value back into the first equation.


{{{m=2(18)-10}}}
{{{m=26}}}


And Mary is 26.


Last step -- Very Important.  Check your answer.


26 = 2 * 18 - 10, 26 = 26 Check and
26 + 5 = 18 + 13, 31 = 31 And both answers check.


Hope that helps,
John