Question 3395
Start by naming the boards, we can call the first board x and the second board y. The problem tells us that x is three feet shorter than twice the length of y. Well, twice the length of y is {{{2y}}} and three feet less than 2y is {{{2y - 3}}}, therefore "x is three feet shorted than twice the length of y" can be written {{{x = 2y - 3}}}. The other part of the problem tells us that together the boards are 15 ft, which means {{{x + y = 15}}}<br>
So what do we have:<br>
<ol>
<li>{{{x = 2y - 3}}} and </li>
<li>{{{x + y = 15}}}</li>
</ol>
Now, let's subtract y from both sides of the second equation. This gives us:<br>
{{{x = 15 - y}}}<br>
Substitute this equation for x into x in the first equation<br>
{{{15 - y = 2y - 3}}}.
add y to both sides to get {{{15 = 3y - 3}}},
add 3 to both sides to get {{{18 = 3y}}},
now divide both sides by 3 to get {{{y = 6}}}.
Substitue y = 6 into the first equation and we get:<br>
{{{x = 2*6 - 3 = 12 - 3 = 9}}}.
So one board is 6 ft and the other is 9 ft.