Select the correct answer.
Bailey has a video streaming service with a flat monthly fee of $18.00 plus an additional cost of $3.50 for each premium movie rental. Bailey can only afford a maximum monthly bill of $40.00.
Which inequality can be used to solve for x, the number of premium movie rentals she can purchase in a month?
A. $18.00x + 3.50 \leq 40.00$
B. $18.00x + 3.50 \geq 40.00$
C. $3.50x + 18.00 \leq 40.00$
D. $3.50x + 18.00 \geq 40.00
Answer (2)
Define the total cost as the sum of the flat fee and the cost of premium movie rentals: Total cost = Flat fee + (Cost per rental) * (Number of rentals).
Express the total cost in terms of the given values and the variable x : Total cost = 18.00 + 3.50 x .
Set up an inequality to represent the condition that the total cost must be less than or equal to the maximum affordable monthly bill: $18.00 + 3.50x
\leq 40.00$.
Rearrange the terms to match one of the given options: 3.50 x + 18.00 ≤ 40.00 . The answer is $\boxed{3.50 x+18.00
\leq 40.00}$.
Explanation
Problem Analysis Let's analyze the problem. Balley has to pay a flat monthly fee of $18.00 for the streaming service. Additionally, she pays $3.50 for each premium movie rental. She wants to keep her monthly bill at or below $40.00. We need to find the inequality that represents this situation, where x is the number of premium movie rentals.
Total Cost Expression The total cost can be represented as the sum of the flat fee and the cost of the movie rentals. The cost of the movie rentals is $3.50 multiplied by the number of rentals, x . So, the total cost is 18.00 + 3.50 x .
Setting up the Inequality Since Balley can only afford a maximum of $40.00, the total cost must be less than or equal to $40.00. This can be written as the inequality: 18.00 + 3.50 x ≤ 40.00 .
Rearranging the Inequality We can also write the inequality as 3.50 x + 18.00 ≤ 40.00 . This matches one of the given options.
Final Answer Therefore, the correct inequality is 3.50 x + 18.00 ≤ 40.00 .
Examples
Imagine you're planning a monthly budget for your entertainment. You have a fixed cost for your internet and want to watch some movies. This problem helps you determine how many movies you can rent without exceeding your budget. Understanding these inequalities can help you manage your expenses and make informed decisions about your entertainment spending.
The correct inequality for Bailey's situation is 3.50 x + 18.00 ≤ 40.00 , which allows her to see how many premium movie rentals she can afford under a $40 budget. This represents the flat fee plus the additional rental costs not exceeding her maximum expenditure. Thus, the correct option to choose is C.
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