If carpet costs thirty-two dollars and fifty cents per square yard, how much would it cost to carpet this room? One of the challenges about this problem is to notice the dimensions of the room are given in feet but the carpet is sold in square yards. So we have two options. We can convert to dimensions to yards first. Or. Or we can determine the area in square feet and then from there determine how many square yards we would need. Now it is true for this example that these dimensions would be pretty easy to convert to yards. But in real life they probably wouldn’t be. Only determine the area in square feet and then determine how many square yards we need.
One other challenge with this problem is the length of this side here is not given. But we should be able to determine it from the given information. Notice how the length of this side here is 15 feet. And the length of this side here is three feet. Now the reason that’s helpful is. If we go to this side here, we know the length from here all the way down to here is 15 feet. We also know the length from here to here is three feet. Well if this is 15 feet and this is three feet. Then that means the length of this side here must be 12 feet. 15 feet minus three feet. Now to determine the area of this L-shaped room what we’re going to do is divided into two different rectangles. And we’ll divide it right here. So the total area will consist of the area of the large rectangle we’ll call area sub one.
And the area of the small rectangle well actually its a square. We’ll call it A sub two. Since the formula for the area of a triangle is length times width. Area sub one is going to be equal to 12 feet times 18 feet. Which will be equal to 216 square feet. And area sub two is a square a three by three squares. So the area of the square would be three times three or nine square feet. So that means a total area of this room would be 216 plus nine square feet. So the area of this room is 225 square feet. Now from here we can determine how many square yards are in 225 square feet. Well one yard is equal to three feet. So if we have a square, let’s called this square three feet by three feet. Which is equal to one yard. We can see that one square yard would be equal to nine square feet. To determine the number of square yards we need to divide 225 by nine. There’s two nine in 22. And there are five nine’s in 45.
So we have a remainder of zero. So 225 square feet is equal to 25 square yards. And so if it cost thirty-two dollars and fifty cents per square yard. The cost is going to be thirty-two fifty times 25. Let’s go determine that cost on the next page. Again the cost is thirty-two dollars and fifty cents per square yard. And we’re going to purchase 25 square yards to carpet this room. Remember, since we have two decimal places here. And zero here. Our product must contain two decimal places as well. So knowing that we’ll go ahead and multiply ignoring the decimal point. And then put the decimal place in the correct position after multiplying. So now we’ll go ahead and multiply by five, we have zero twenty-five carry the two. Five times two plus two that’s 12. Carry a one. Five times three plus one that would be 16. Now we’ll multiply by two. Well we need to make sure that the first digit goes in this column here.
So two times zero would be zero. Two times five is ten. Carry a one. Two times two plus one that’s five. And two times three would be six. Now we’ll add zero five two 11 carry the one. And eight. Right now the decimal point is here. But since we have to have two decimal places rather decimal point we’ll move it over two places to here. So the total cost to replace the carpet in that one room. Is going to be eight hundred twelve dollars and fifty cents. .