Problem 314 - Elementary Algebra

Question

In the following exercises, solve. Teegan likes to play golf. He has budgeted \(\$ 60\) next month for the driving range. It costs him \(\$ 10.55\) for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?

Step-by-Step Solution

Answer

Teegan can go to the driving range a maximum of 5 times next month.

Step 1 - Identify the total budget

Teegan has a total budget of \( \$60 \) for the driving range next month.

Step 2 - Identify the cost per visit

It costs \( \$10.55 \) for each bucket of balls Teegan buys when he goes to the driving range.

Step 3 - Set up the inequality

To find the maximum number of times Teegan can go, set up the inequality: \( 10.55x \leq 60 \), where \(x\) is the number of times he goes.

Step 4 - Solve the inequality

Solve for \(x\) by dividing both sides of the inequality by 10.55: \[ x \leq \frac{60}{10.55} \]

Step 5 - Calculate the maximum number of times

Calculate \( \frac{60}{10.55} \) to determine the maximum number of visits: \[ x \leq 5.687 \approx 5 \text{ (since Teegan cannot make a partial visit)} \]

Key Concepts

budgeting

Budgeting is an essential skill for managing finances. It involves planning how to spend your money over a given period. In Teegan's case, he has allotted \( \$60 \) for his driving range visits next month. This means he cannot exceed this amount or he will overspend.

• First, identify your total available funds, which in this exercise is \( \$60 \).
• Next, list all expenses related to the activity, such as the cost per visit to the driving range.

Budgeting helps you keep track of your spending, ensuring you only spend within your allocated amount. It's crucial to distinguish between different types of expenses and prioritize accordingly. For Teegan, the priority is sticking to his \( \$60 \) budget.

cost analysis

Cost analysis is the process of determining the costs involved in an activity or business operation. For Teegan, this means understanding the cost of each visit to the driving range. It costs him \( \$10.55 \) for each bucket of balls.

• Identify fixed and variable costs. In this scenario, \( \$10.55 \) is a fixed cost per visit.
• Calculate how these costs add up over multiple visits.

Performing a cost analysis helps you understand the financial implications of your activities. Teegan uses this to determine how many times he can visit the driving range without exceeding his budget.

maximum number of visits

Determining the maximum number of visits that fit within a budget involves solving an inequality. In Teegan's case, the inequality is \( 10.55x \leq 60 \), where \( x \) represents the number of visits. To solve:

• Set up the inequality based on the cost per visit and the total budget: \( 10.55x \leq 60 \).
• Divide both sides by the cost per visit to isolate \( x \): \( x \leq \frac{60}{10.55} \).
• Calculate the result: \( \frac{60}{10.55} \approx 5.687 \), which rounds down to 5 since partial visits are not possible.

Thus, Teegan can visit the driving range a maximum of 5 times within his budget. This method ensures you maximize the number of visits without going over the allocated amount.