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. (7.EE.4 a, b) 3 pts Write an inequality that represents this real-world situation.
Answers
GPT-4o mini
To represent the situation with an inequality, we can start by breaking down the costs involved. The total cost \(C\) for hiring the landscaping company is made up of a consultation fee of $50 and a charge of $20 per hour worked. This can be represented with the following formula:
\[
C = 50 + 20h
\]
We want to find out how many hours \(h\) can be worked such that the total cost does not exceed $150. Therefore, we set up the inequality:
\[
50 + 20h \leq 150
\]
Now, we will solve this inequality for \(h\):
1. Subtract 50 from both sides:
\[
20h \leq 150 - 50
\]
\[
20h \leq 100
\]
2. Now, divide both sides by 20:
\[
h \leq \frac{100}{20}
\]
\[
h \leq 5
\]
### Interpretation of the Solution:
The solution \(h \leq 5\) means that you can work at most 5 hours to keep the total cost for hiring the landscaping company at $150 or less. If you work more than 5 hours, the cost will exceed $150, which is not desirable in this scenario. Thus, the landscaping company can work from 0 hours up to 5 hours under the budget constraint provided.
\[
C = 50 + 20h
\]
We want to find out how many hours \(h\) can be worked such that the total cost does not exceed $150. Therefore, we set up the inequality:
\[
50 + 20h \leq 150
\]
Now, we will solve this inequality for \(h\):
1. Subtract 50 from both sides:
\[
20h \leq 150 - 50
\]
\[
20h \leq 100
\]
2. Now, divide both sides by 20:
\[
h \leq \frac{100}{20}
\]
\[
h \leq 5
\]
### Interpretation of the Solution:
The solution \(h \leq 5\) means that you can work at most 5 hours to keep the total cost for hiring the landscaping company at $150 or less. If you work more than 5 hours, the cost will exceed $150, which is not desirable in this scenario. Thus, the landscaping company can work from 0 hours up to 5 hours under the budget constraint provided.