document.write( "Question 111467: The difference of two numbers is 7. The second is 7 less than 2 times the first. What are the two numbers? \n" ); document.write( "

Algebra.Com's Answer #81298 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
You need to first express the problem symbolically. First thing you need are symbols for the two numbers, so let's call them $\"n%5B1%5D\"$ and $\"n%5B2%5D\"$ .
\n" ); document.write( ":
\n" ); document.write( "The first fact we know is that the difference of these two numbers is 7. So, let's call $\"n%5B2%5D\"$ the larger of the two numbers, so we can write $\"n%5B2%5D-n%5B1%5D=7\"$
\n" ); document.write( ":
\n" ); document.write( "Our next fact says \"The second is 7 less than 2 times the first.\" So let's write:
\n" ); document.write( " $\"n%5B2%5D=2n%5B1%5D-7\"$
\n" ); document.write( ":
\n" ); document.write( "Since the second equation gives us an expression for $\"n%5B2%5D\"$ directly, let's just substitute into the first equation:
\n" ); document.write( ":
\n" ); document.write( " $\"2n%5B1%5D-7-n%5B1%5D=7\"$
\n" ); document.write( ":
\n" ); document.write( "Add 7 to both sides and collect terms to get:
\n" ); document.write( ":
\n" ); document.write( " $\"n%5B1%5D=14\"$
\n" ); document.write( ":
\n" ); document.write( "Now put this value back into equation 1:
\n" ); document.write( ":
\n" ); document.write( " $\"n%5B2%5D-14=7\"$ , so
\n" ); document.write( " $\"n%5B2%5D=21\"$
\n" ); document.write( ":
\n" ); document.write( "Last step, check your answer.
\n" ); document.write( ":
\n" ); document.write( " $\"21-14=7\"$ , and
\n" ); document.write( " $\"21=2%2814%29-7\"$ . Since both of those statements are true, the answer checks.
\n" ); document.write( " \n" ); document.write( "

\n" );