Question 249094
Let x=the first number, y=second number


The phrase "One number is 5 more than another" can be broken up as:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/translation1.png">



So "One number is 5 more than another" translates to {{{x=5+y}}}


Note: this implies that {{{x>y}}} ie 'y' is the smaller number.



Similarly, "5 times the smaller equals 4 times the larger" can be represented as


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/translation2.png">



So "5 times the smaller equals 4 times the larger" translates to {{{5y=4x}}}



So we have the two equations {{{system(x=5+y,5y=4x)}}}



{{{x=5+y}}} Start with the first equation.



{{{x-5=y}}} Subtract 5 from both sides.



{{{y=x-5}}} Rearrange the equation.



{{{5y=4x}}} Move onto the second equation.



{{{5(x-5)=4x}}} Plug in {{{y=x-5}}} (this works since we're dealing with the same 'y').



{{{5x-25=4x}}} Distribute.



{{{5x=4x+25}}} Add {{{25}}} to both sides.



{{{5x-4x=25}}} Subtract {{{4x}}} from both sides.



{{{x=25}}} Combine like terms on the left side.



{{{y=x-5}}} Go back to the first isolated equation.



{{{y=25-5}}} Plug in {{{x=25}}}



{{{y=20}}} Subtract.



So the solutions are {{{x=25}}} and {{{y=20}}} giving us the ordered pair (25,20)



So the smaller number is 20 and the larger is 25.