Problem 76 - Prealgebra

Question

Children's tickets to the movies go on sale for \(\$ 4.75 .\) The Lions club of Alameda has \(\$ 800\) set aside to purchase these tickets. Approximately how many tickets can the Lions club of Alameda purchase?

Step-by-Step Solution

Answer

The Lions club can purchase 168 tickets.

Step 1: Identify the Ticket Price and Budget

The problem is asking for the number of children's movie tickets that can be purchased. We are given that each ticket costs \( \\(4.75 \) and the Lions club has a budget of \( \\)800 \).

Step 2: Set Up the Division Problem

To find the number of tickets that can be purchased, we need to divide the total budget by the price per ticket. This can be written as the division \( \frac{800}{4.75} \).

Step 3: Perform the Division

Calculate \( \frac{800}{4.75} \) using a calculator or long division. The result is approximately \( 168.42 \).

Step 4: Approximate the Result

Since you cannot purchase a fraction of a ticket, round the result of \( 168.42 \) down to the nearest whole number. Thus, the number of tickets the Lions club can purchase is 168.

Key Concepts

Division in Mathematics

Division is a fundamental concept in mathematics that allows us to determine how many times one number can be contained within another. It involves dividing a larger number (the dividend) by a smaller number (the divisor) to find the quotient. In our exercise, the dividend is the total budget, \(800\), and the divisor is the price of one ticket, \(4.75\). This division problem can be represented as \(\frac{800}{4.75}\).

When solving division problems, keep these tips in mind:

• Ensure both numbers are in the same unit (in this case, dollars).
• Use long division or a calculator for precise calculations.
• Understand that the quotient represents how many times the divisor fits into the dividend.

In practical terms, division helps us in scenarios like determining the number of items we can purchase within a certain budget.

Budgeting Problems

Budgeting is all about managing resources within their limits. It’s a real-world application of mathematical operations like division. Budgeting problems often require us to divide a total amount of money by the cost of individual items to determine how many items can be purchased.

In our example, the Lions Club of Alameda is trying to decide how many children's movie tickets they can buy with a budget of \(800\). Solving budgeting problems involves several steps:

• Identify the total resources available (the budget).
• Know the cost of each individual item.
• Use division to determine the maximum number of items that can be purchased without surpassing the budget.

Always round down the quotient to avoid overspending, since you cannot buy a portion of an item like a ticket.

Approximation in Mathematics

Approximation is crucial in situations where exact figures are impractical. It helps simplify calculations and make decisions based on limited data or constraints. When working with division in real-world scenarios, results often come out as fractions.

For instance, dividing \(800\) by \(4.75\) yields approximately \(168.42\). However, you cannot buy a fraction of a ticket, so we approximate by rounding down to \(168\), ensuring the spending does not exceed the budget.

When using approximation:

• Consider whether to round up or down based on the context.
• Rounding down is common in budgeting to prevent overspending.
• Approximation allows for efficient decision-making, especially in financial contexts.

Understanding when and how to use approximation is crucial for accurate and practical problem-solving in mathematics.