Question

Translate to an equation and solve. A football quarterback in one game completes \(34 \%\) of his pass attempts. If he completed 14 passes, how many pass attempts did he have in the game?

Short answer

Answer: 41 pass attempts

Step-by-step solution

Write the equation representing the problem.

Let x represent the total number of pass attempts. Since the football quarterback completed 34% of his pass attempts, we can write the equation: \(0.34x = 14\)

Solve the equation for x.

To solve for x, we can simply divide both sides of the equation by 0.34: \(x = \frac{14}{0.34}\) Calculating the fraction: \(x \approx 41.18\)

Round to the nearest whole number.

Since the number of pass attempts must be a whole number, we can round up to the nearest whole number: \(x \approx 41\) So the football quarterback had approximately 41 pass attempts in the game.

Key concepts

Understanding Percentage Problems

When faced with percentage problems, what we're primarily dealing with is a way to express a number as a fraction of 100. For instance, saying a quarterback completed 34% of his passes means he successfully threw 34 out of every 100 attempts. This concept can be applied to various scenarios, such as calculating discounts in shopping, understanding statistics, or assessing success rates like in sports.

For our specific problem about the quarterback, we knew he completed 14 passes which represented 34% of all his attempts. Using this, we set up the equation based on the formula:

• Completing passes = Percentage \( imes \) Total attempts

In mathematical terms, it looks like this: \(0.34 \times x = 14\)Where:

• \(x\) is the total number of pass attempts.

Basics of Algebra in Solving Equations

Basic algebra is a crucial skill for solving equations, allowing us to solve for unknown variables. Here, you're generally rearranging an equation to isolate the variable and find its value. Let's revisit the equation from the quarterback example:\(0.34x = 14\)The aim is to find \(x\), which represents the total pass attempts. To isolate \(x\), we perform the inverse operation. Multiplying by 0.34 means we should divide both sides by 0.34 to solve for \(x\). This gives:\(x = \frac{14}{0.34}\)Solving this division provides the total number of pass attempts. This approach using algebra is quite universal for problems where you need to find a missing value.

Solving Word Problems Effectively

Word problems often combine math concepts with real-world scenarios, requiring you to translate a narrative into a solvable equation. The key steps involve:

• Identifying what you know and what you need to find out.
• Translating words into a mathematical equation.
• Solving the equation step by step.

In the quarterback problem, the narrative is about completed pass attempts, represented as a percentage of total attempts. From the problem, we know the quarterback completed 14 passes, equivalent to 34%. This information helped us create an equation to solve for the unknown total number of attempts.

This method can be applied to diverse contexts, such as budgeting or travel time calculations. Effective handling of word problems hinges on properly interpreting the question and then using math to find the solution.