  # Math Question

<p>I don't know how approach this. Well I kinda do, but can someone give me a detailed explanation on how to do this? </p>

<p>The cost of a piece of a certain type of lumber is directly proportional to its length. A piece of lumber that is 8 feet long costs \$6.00. What is the cost, in dollars, of a piece of this lumber that is y yards long? (1 yd = 3 ft)</p>

<p>Ok well "directly proportional" indicates a relationship including y=kx where "K" is the constant that relates X and Y. Because it is directly proportional, you can use proportions to find the answer. Since 8ft of lumber costs 6 dollars, 3Y will be equal Z dollars. We're solving for Z. (Note: I used 3Y because the original given was in feet, and they ask yards, you must have equal units.)</p>

<p>So 8 ft / 6 dollars = 3Y ft / Z dollars</p>

<p>If you cross multiply you find that 8Z=18Y.
Since you're solving for Z, divide both sides by 8.
So a piece of lumber that is Y yards long will cost 2.25Y. Meaning every yard costs 2.25 dollars.</p>

<p>The way I'd solve it. You are looking for yards. So, you have 6 dollars and 2 2/3 yards (8 feet). 6 divided by 2&2/3= 2.25</p>

<p>I don't like setting up Xs and Ys.</p>

<p>Find the cost per foot, then multiply by 3 to find the cost per yard.</p>