Question 92430
One number is 12 more than another:
{{{x = 12 + y}}}
Sum of the smaller number (y) and twice the larger number (x) is 39:
{{{y + 2x = 39}}}


Find the larger.  Start by taking the second equation and solving for x by subtracting y from both sides:
{{{2x = 39 - y}}}
Then divide both sides by 2 to get the x by itself:
{{{x = (39 - y)/2}}}


Now you can substitute that answer into the first equation:
{{{(39 - y)/2 = 12 + y}}}
Multiply both sides by 2 to get rid of the denominator:
{{{39 - y = (12 + y)2}}}
{{{39 - y = 24 + 2y}}}
Add y to both sides:
{{{39 = 24 + 2y + y}}}
{{{39 = 24 + 3y}}}
Subtract 24 from both sides:
{{{39 - 24 = 3y}}}
{{{15 = 3y}}}
{{{5 = y}}}

Now you can plug in the value for y to get the answer:
{{{x = 12 + y}}}
{{{x = 12 + 5}}}
{{{x = 17}}}