Question 719957
Here we go. Let's let x be the larger of the two numbers. For now we'll let t be the amount we can subtract from x to get the smaller of the 2 numbers. So 
{{{x+(x-t)=100}}}
{{{2*x-t=100}}}
{{{x=(100+t)/2}}}

We next just put the ratio sentence into an equation we get
{{{(x+5)/(x-t-5)=4}}}

Well we know what x is in terms of t so we substitute that and get
{{{((100+t)/2+5)/((100+t)/2-t-5)=4}}}
{{{50+t/2+5=4*(50+t/2-t-5)}}}
{{{50+t/2+5=200+2t-4t-20}}}
{{{t/2-2t+4t=200-20-50-5}}}
{{{t/2+4t/2=125}}}
{{{5t/2=125}}}
{{{5t=250}}}
{{{t=50}}}
so {{{x=(100+50)/2=75}}}


If the large number is 75 we easily get the small number is 25. The two numbers clearly work.(80/20=4).