The Texas club is sponsoring a bake sale. If their goal is to raise at least $450, how many pastries (P) must they sell at [tex]$9.00[/tex] each in order to meet that goal?
A. [tex]$P \leq 50$[/tex]
B. [tex]$P \geq 50$[/tex]
C. [tex]$P \ \textless \ 50$[/tex]
D. [tex]$P\ \textgreater \ 150$[/tex]
Answer (1)
Define P as the number of pastries to sell.
Set up the inequality 9.00 × P \tgeq 450 .
Solve the inequality by dividing both sides by 9.00 , resulting in P \tgeq 50 .
The Texas club must sell at least 50 pastries: P \tgeq 50 .
Explanation
Problem Analysis Let's analyze the problem. The Texas club wants to raise at least $450 from a bake sale. They are selling pastries for $9.00 each. We need to find the minimum number of pastries they must sell to reach their goal.
Setting up the Inequality Let P be the number of pastries they need to sell. The total revenue from selling P pastries is 9.00 × P . To meet their goal, the revenue must be at least 450. T hi sc anb e w r i tt e na s anin e q u a l i t y : 9.00 × P \tgeq 450 $
Solving the Inequality Now, let's solve the inequality for P . Divide both sides of the inequality by 9.00 :
9.00 9.00 × P \tgeq 9.00 450 P \tgeq 50
Interpreting the Solution The inequality P \tgeq 50 means that the Texas club must sell at least 50 pastries to meet their goal of raising at least $450.
Final Answer Therefore, the correct answer is P \tgeq 50 .
Examples
Imagine you are organizing a school fundraiser. You need to raise a certain amount of money, and you are selling tickets for a specific price. This problem helps you determine the minimum number of tickets you need to sell to reach your fundraising goal. For example, if you need to raise $1000 and each ticket costs $5, you would need to sell at least 200 tickets ($5 \times 200 = $1000). Understanding how to set up and solve these types of inequalities can help you plan and manage your fundraising efforts effectively.
