Problem 5 - Prealgebra

Question

Express each rate as a unit rate. Round to the nearest tenth, if necessary. \(\$ 183\) for 4 concert tickets

Step-by-Step Solution

Answer

The unit rate is $45.8 per concert ticket.

Step 1: Identify the Given Rate

The problem provides that 4 concert tickets cost $183. This is a rate, which we need to express as a unit rate.

Step 2: Define Unit Rate

A unit rate is a rate in which the second quantity is 1. For this problem, we need to find the cost for 1 concert ticket.

Step 3: Calculate the Unit Rate

To find the unit rate, divide the total cost by the number of tickets: \[\text{Cost per ticket} = \frac{183}{4}\]

Step 4: Perform the Division

Divide \(183 by 4 to find the cost of one ticket: \[183 \div 4 = 45.75\]This gives us a unit rate of \)45.75 per ticket.

Step 5: Round to the Nearest Tenth

Since the result is already at a tenth due to the 0.75, rounding 45.75 to the nearest tenth remains 45.8.

Step 6: Conclude with the Unit Rate

Thus, the cost of each concert ticket, when rounded to the nearest tenth, is $45.8.

Key Concepts

Rate Calculation

In everyday life, we often come across rates, as they help us understand relationships between quantities, like price per item or speed per hour. Here, the challenge is to convert a given rate into a unit rate. The unit rate shows us the value of a single unit of one quantity and is achieved by dividing the first quantity by the second.

• The given rate in this instance is $183 for 4 concert tickets.
• To convert this rate into a unit rate, we need to find out how much one ticket costs.

By performing the calculation, we understand the individual expense per concert ticket, providing a clearer view into the value each ticket holds. Taking such steps represents an essential approach to achieving value comprehension in context.

Division

To uncover the unit rate, division plays a critical role in breaking down the overall rate. Division allows one to distribute a cost or quantity evenly amongst single units. For this exercise, we divided the total cost, $183, by the number of tickets, 4.

• This is calculated as: \[183 \div 4 = 45.75\]

Division simplifies complex rates into manageable units, enabling us to easily assess the value of each component. This process ensures we assign the correct price to each ticket, offering insights for informed decision-making.

Rounding Numbers

In mathematics, rounding numbers makes them simpler to work with while retaining their approximate value, especially important for clear communication of costs. The division yielded a result of 45.75. However, for simplicity and standard representation, this number can be rounded.

• Rounding to the nearest tenth involves looking at the hundredths place: if it's 5 or more, round up. If it’s less, round down.
• Here, since 75 hundredths means the number is closer to 46 tenths, 45.75 rounds to 45.8.

Rounding helps us convey figures in a more digestible manner, assisting in better applying them in daily applications, such as planning for concert expenses.