3. The rental cost for a floor sander is given by the following equation:

[tex]\[ C = 4.5h + 10.00 \][/tex]

where [tex]\( C \)[/tex] is the total cost in dollars and [tex]\( h \)[/tex] is the number of hours that you use the floor sander. If you have budgeted only \$45 for renting the floor sander, what is the maximum number of hours that you can rent it?



Answer :

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.