Mrs. Webb paid $225 for 450 square feet of carpet. If she needs 200 additional square feet of carpet, how much extra will it cost?
Understand the Problem
The question is asking us to determine the additional cost for 200 square feet of carpet based on the price per square foot calculated from the initial purchase. We will first find the cost per square foot and then multiply that by the additional square feet needed.
Answer
The additional cost for 200 square feet of carpet is given by \( \frac{C \times 200}{A} \).
Answer for screen readers
The additional cost for 200 square feet of carpet is given by:
$$ \text{Additional Cost} = \frac{C \times 200}{A} $$
Steps to Solve
- Calculate the Cost per Square Foot
We need to determine the cost per square foot of the initial carpet purchase. If the total cost of the carpet is given, we divide it by the total square footage purchased.
Assuming the total cost is $C$ and the total square footage is $A$, the formula is:
$$ \text{Cost per square foot} = \frac{C}{A} $$
- Determine the Additional Cost for 200 Square Feet
Once we have the cost per square foot, we can find the additional cost for 200 square feet. We multiply the cost per square foot by the additional square footage.
Let the cost per square foot be represented as $P$. Then the calculation for the additional cost becomes:
$$ \text{Additional Cost} = P \times 200 $$
- Calculate the Final Additional Cost
Substituting the expression for cost per square foot into the additional cost formula, we get:
$$ \text{Additional Cost} = \left( \frac{C}{A} \right) \times 200 $$
This gives us the formula to compute the additional cost based on our initial purchase values.
The additional cost for 200 square feet of carpet is given by:
$$ \text{Additional Cost} = \frac{C \times 200}{A} $$
More Information
This formula allows us to quickly find out how much it would cost to buy additional carpet given the original purchase details. By knowing the cost and area of the initially purchased carpet, we can easily expand the area we want to cover without much hassle.
Tips
- Forgetting to use the correct values for total cost or area when calculating the cost per square foot.
- Not converting units if the area is not in square feet when performing calculations.
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