Well, this problem is really stumping me, so here it is.
Directions: In each problem, first draw a picture of the situation to the right of the problem. Then decide whether the problem involves measuring length or area growth to help you answer the questions.
1. It costs Mrs. Jones $400 to carpet the small room shown. She has another room twice as long and twice as wide. How much will it cost her to carpet the bigger room with carpeting?
The picture shows a rectangle with no shown dimensions.
So, how am I suppose to start off?
-Sorry for the grammar mis-splled, I just type-read from the paper.
For this problem you need the area to find how much carpet is needed. Since I'm not a math teacher, I had to try a few possible dimensions to form a conclusion.
If the small room were 10 feet by 10 feet, then its area is 100 square feet.
That means the large room is 20 by 20 or 400 square feet.
Conclusion: it will cost 4 times as much to carpet the large room.
Would it be $800?
When I went to school 4 times 400 was not 800.
It says twice as wide, not four times..
Nevermind, it says twice as long/wide.
let the original be x by y, so the area is xy
the new is 2x by 2y , so the new area is 4xy
so it is 4 times as large, as Ms Sue told you
No worries about the grammar. Let's break down the problem and find the solution step by step.
1. Start by drawing a picture of the small room that is given in the problem. Since the dimensions of this room are not provided, simply draw a rectangle to represent it.
2. Based on the given information, we know that Mrs. Jones has another room that is twice as long and twice as wide as the small room. In terms of area, if the small room has an area of A, then the bigger room will have an area of 2A.
3. Now, we need to determine whether the problem involves measuring length or area growth to answer the question. In this case, since we are dealing with carpeting, which is typically sold by the square foot or square meter, we are interested in finding the area.
4. Next, we need to find the cost of carpeting the small room to help us find the cost of carpeting the bigger room. According to the problem, it costs Mrs. Jones $400 to carpet the small room.
5. Since the bigger room has an area of 2A, we can set up a proportion to find the cost of carpeting the bigger room. The proportion is:
Cost of carpeting the small room / Area of the small room = Cost of carpeting the bigger room / Area of the bigger room
Plugging in the values we know, we have:
$400 / A = Cost of carpeting the bigger room / 2A
6. To solve for the cost of carpeting the bigger room, we can cross-multiply and solve the equation:
$400 * 2A = A * Cost of carpeting the bigger room
800A = A * Cost of carpeting the bigger room
7. Simplifying the equation, we see that A cancels out, leaving us with:
800 = Cost of carpeting the bigger room
Therefore, it will cost Mrs. Jones $800 to carpet the bigger room with carpeting.
To summarize, to find the solution to this problem:
- Draw a picture of the given small room.
- Determine that the problem involves measuring area growth.
- Find the cost of carpeting the small room.
- Set up a proportion using the areas of the small room and the bigger room.
- Solve the proportion equation to find the cost of carpeting the bigger room, which in this case is $800.