The Magic Carpet charges $90 for installation and $9 per square yard of carpeting. If the total cost to carpet an office is $810, how many square yards is the office?
Understand the Problem
The question is asking to find the number of square yards of carpeting needed for an office based on the total cost, which includes a fixed installation fee and a variable cost per square yard. We will set up an equation to solve for the number of square yards.
Answer
$80$
Answer for screen readers
The number of square yards of carpeting needed is $80$.
Steps to Solve
- Identify the variables and costs
Let $x$ be the number of square yards of carpeting. The total cost equation can be set up as follows: Total cost = Installation cost + Cost per square yard
Given:
- Installation cost = $90
- Cost per square yard = $9
- Set up the equation
Using the information provided, the equation for the total cost is: $$ 90 + 9x = 810 $$
- Solve for $x$
To find $x$, first, isolate it by subtracting the installation cost from both sides: $$ 9x = 810 - 90 $$
Calculate the right side: $$ 9x = 720 $$
- Divide to find $x$
Now, divide both sides by 9 to solve for $x$: $$ x = \frac{720}{9} $$
- Calculate the final answer
Perform the division: $$ x = 80 $$
The number of square yards of carpeting needed is $80$.
More Information
The total cost to carpet an office includes both a fixed installation fee and the per square yard cost of carpeting. This example illustrates how to set up and solve a simple linear equation.
Tips
- Forgetting to subtract the installation fee before solving for $x$.
- Incorrectly calculating the division when isolating $x$.
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