Certainly! Let's break down the problem step-by-step.
1. You are provided with the equation for the rental cost of a floor sander:
[tex]\[
C = 4.5h + 10
\][/tex]
Here, [tex]\(C\)[/tex] represents the total cost in dollars, and [tex]\(h\)[/tex] denotes the number of hours you rent the floor sander.
2. You have a predefined budget, which is [tex]$45.
3. Our goal is to determine the maximum number of hours (\(h\)) you can rent the floor sander without exceeding your $[/tex]45 budget.
4. Substitute the given budget into the cost equation:
[tex]\[
45 = 4.5h + 10
\][/tex]
5. Now, solve this equation for [tex]\(h\)[/tex].
6. First, isolate the term involving [tex]\(h\)[/tex] by subtracting the fixed cost from both sides:
[tex]\[
45 - 10 = 4.5h
\][/tex]
Simplify the left side:
[tex]\[
35 = 4.5h
\][/tex]
7. Solve for [tex]\(h\)[/tex] by dividing both sides of the equation by the cost per hour:
[tex]\[
h = \frac{35}{4.5}
\][/tex]
8. Now, divide 35 by 4.5:
[tex]\[
h \approx 7.777777777777778
\][/tex]
Hence, the maximum number of hours that you can rent the floor sander without exceeding your $45 budget is approximately 7.78 hours.
