Question
A landscaping company charges $20 per hour of work plus a $50 consultation fee. Write and solve an inequality to find the number of hours, h, you need to work to spend no more than $150. Interpret your solution in the context of the problem
Answers
GPT-4o mini
To determine the maximum number of hours \( h \) that you can hire the landscaping company without exceeding a total spend of $150, we first need to set up the cost equation based on the company's charges.
The total cost \( C \) for hiring the company can be expressed as:
\[
C = 20h + 50
\]
where \( 20h \) is the charge for \( h \) hours of work, and $50 is the consultation fee.
Since we want to spend no more than $150, we can set up the following inequality:
\[
20h + 50 \leq 150
\]
Now, let's solve the inequality:
1. Subtract 50 from both sides:
\[
20h \leq 150 - 50
\]
\[
20h \leq 100
\]
2. Divide both sides by 20:
\[
h \leq \frac{100}{20}
\]
\[
h \leq 5
\]
The solution \( h \leq 5 \) means that you can hire the landscaping company for a maximum of 5 hours in order to spend a total cost of no more than $150.
### Interpretation in the Context of the Problem
In practical terms, this means that if you want to keep your total expenditure for landscaping services (including the consultation fee) to $150 or less, you can afford to have the landscaping company work for up to 5 hours. If you hire them for more than 5 hours, the total cost would exceed your budget.
The total cost \( C \) for hiring the company can be expressed as:
\[
C = 20h + 50
\]
where \( 20h \) is the charge for \( h \) hours of work, and $50 is the consultation fee.
Since we want to spend no more than $150, we can set up the following inequality:
\[
20h + 50 \leq 150
\]
Now, let's solve the inequality:
1. Subtract 50 from both sides:
\[
20h \leq 150 - 50
\]
\[
20h \leq 100
\]
2. Divide both sides by 20:
\[
h \leq \frac{100}{20}
\]
\[
h \leq 5
\]
The solution \( h \leq 5 \) means that you can hire the landscaping company for a maximum of 5 hours in order to spend a total cost of no more than $150.
### Interpretation in the Context of the Problem
In practical terms, this means that if you want to keep your total expenditure for landscaping services (including the consultation fee) to $150 or less, you can afford to have the landscaping company work for up to 5 hours. If you hire them for more than 5 hours, the total cost would exceed your budget.