Question 939861

let Ben's age be {{{B}}} and Josh's age {{{J}}}

if Ben is four years older than Josh, then we have 

{{{B=J+4}}}.....eq.1

if the product of their ages is {{{437}}}, then we have


{{{B*J=437}}}.....eq.2 ....substitute {{{J+4}}} for {{{B}}} from eq.1

{{{(J+4)*J=437}}}.....solve for {{{J}}}

{{{J^2+4J=437}}}

{{{J^2+4J-437=0}}}...use quadratic formula

{{{J = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{J = (-4 +- sqrt( 4^2-4*1*(-437) ))/(2*1) }}} 

{{{J = (-4 +- sqrt( 16+1748 ))/2 }}} 

{{{J = (-4 +- sqrt( 1764 ))/2 }}}

{{{J = (-4 +- 42)/2 }}}
 
solution: we will nee only positive solution since age cannot be negative

{{{J = (-4 + 42)/2 }}}

{{{J = 38/2 }}}

{{{highlight(J = 19) }}}

now find Ben's age:

{{{B=J+4}}}.....eq.1

{{{B=19+4}}}

{{{highlight(B=23)}}}