Question 1134351


let Jim's age be {{{J}}} and Colleens's age {{{C}}}

if Jim is a year older than Colleen, we have {{{J=C+1}}}

 and the {{{difference}}} of the squares of their ages is {{{97}}}, we have

{{{J^2-C^2=97}}}...solve for {{{C}}}

{{{C^2=J^2-97}}}...........substitute {{{J=C+1}}}

{{{C^2=(C+1)^2-97}}}.......solve for {{{C}}}

{{{C^2=C^2+2C+1-97}}}
{{{C^2=C^2+2C-96}}}
{{{C^2-C^2-2C+96=0}}}

{{{-2C+96=0}}}

{{{2C=96}}}...simplify

{{{C=48}}}->Colleens's age
{{{J=48+1}}}->{{{J=49}}}->Jim's age