Which equation represents the following word problem?
A school sells pencils to students for 25 cents each. If a student has $9, how many pencils can the student buy?
$(.25) p=9$
$\frac{p}{.25}=9$
$p-.25=9$
$p+.25=9$
Answer (2)
The price of each pencil is $0.25.
The student has $9 to spend.
The equation representing the situation is 0.25 p = 9 .
Therefore, the equation is ( .25 ) p = 9 .
Explanation
Problem Analysis Let's analyze the problem. We are given that each pencil costs 25 cents, which is equivalent to $0.25. A student has a total of $9 to spend on pencils. We need to determine which equation correctly represents this scenario, where 'p' represents the number of pencils the student can buy.
Formulating the Equation If a student buys 'p' pencils at $0.25 each, the total cost will be $0.25 multiplied by 'p', which is 0.25 p . The student can spend at most $9, so the total cost must equal $9. Therefore, the equation that represents this situation is 0.25 p = 9 .
Identifying the Correct Equation The correct equation is ( 0.25 ) p = 9 .
Examples
Imagine you're organizing a school fundraiser where you're selling cookies for $0.75 each, and you want to figure out how many cookies you need to sell to reach a fundraising goal of $300. This problem is similar; you'd set up an equation where $0.75 times the number of cookies equals $300. Solving this helps you plan your sales strategy effectively. Understanding how to set up and solve these equations is crucial for managing budgets, planning events, and making informed financial decisions in everyday life.
The equation that represents the situation is ( 0.25 ) p = 9 , indicating that if each pencil costs 25 cents, the total cost for 'p' pencils must equal $9. Therefore, the correct choice from the given options is this equation. By solving this equation, you can find out how many pencils the student can purchase with $9.
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