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 (2)
Set up an inequality representing the problem: $9P
ge 450 , w h ere P$ is the number of pastries.
Divide both sides of the inequality by 9 to solve for P : $P
ge \frac{450}{9}$.
Simplify the fraction: $P
ge 50$.
The Texas club must sell at least 50 pastries: $\boxed{P
ge 50}$.
Explanation
Understanding the Problem The Texas club is holding a bake sale to raise money. Their goal is to raise at least $450. They are selling each pastry for $9. We need to determine 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 amount of money they raise will be the number of pastries sold multiplied by the price of each pastry, which is $9. We want this total to 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 P g e 450 $
Solving for P To find the minimum number of pastries, we need to solve the inequality for P . We can do this by dividing both sides of the inequality by 9: 9 9 P g e 9 450 P g e 50
Interpreting the Solution The inequality $P
ge 50$ means that the Texas club must sell at least 50 pastries to meet their goal of raising at least $450.
Examples
Imagine you are organizing a school fundraiser. You need to raise a certain amount of money, and you are selling items at a set price. This problem helps you determine the minimum number of items you need to sell to reach your fundraising goal. For example, if you need to raise $300 and you are selling cookies for 5 e a c h , yo u w o u l d n ee d t ose ll a tl e a s t 60 coo ki es b ec a u se \frac{300}{5} = 60$. Understanding how to set up and solve these types of inequalities can help you plan and manage successful fundraising events.
The Texas club must sell at least 50 pastries to meet their fundraising goal of $450. Therefore, the correct answer is option B: P ≥ 50.
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