Question 1135028

let two numbers be {{{x}}} and {{{y}}}, and let {{{x}}} be the larger number

given:
The sum of two numbers is sixty-five. 
{{{x+y=65}}}...solve for {{{x}}}

{{{x=65-y}}}.......eq.1

If the larger number is divided by the smaller number, then the quotient is three and the remainder is five. 

{{{x/y=3 +5/y}}}..solve for {{{x}}}

{{{x=3y +5y/y}}}
{{{x=3y +5}}}...............eq.2

from eq.1 and eq.2 we have:


Find the numbers{{{3y +5=65-y}}}

{{{3y +y=65-5}}}

{{{4y=60}}}

{{{y=60/4}}}

{{{highlight(y=15)}}}

go back to {{{x=65-y}}}.......eq.1, plug in {{{y}}} value and find {{{x}}}

{{{x=65-15}}}

{{{highlight(x=50)}}}

so, your numbers are: {{{highlight( 50)}}} and {{{highlight(15)}}}


check:
{{{x+y=65}}}
{{{50+15=65}}}
{{{65=65}}}

{{{x/y=3 +5/y}}}
{{{50/15=3 +5/15}}}
{{{50/15=3 +1/3}}}
{{{3.333333333333333=3 +0.333333333333333}}}
{{{3.333333333333333=3.333333333333333}}}