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Chapter 7: Problem 4

If one movie ticket costs \(\$ 13.50,\) how much will \(y\) tickets cost?

Short Answer

Expert verified
Total Cost = 13.50y

Step by step solution

01

Identify the given information

The cost of one movie ticket is given as \( \$13.50 \).
02

Define the variable

Let \(y\) represent the number of tickets.
03

Set up the equation

The total cost for \(y\) tickets can be calculated by multiplying the cost of one ticket by the number of tickets: \( \text{Total Cost} = \$13.50 \times y \).
04

Write the final expression

Substitute the given values into the equation to get: \[ \text{Total Cost} = 13.50y \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variable Representation
In algebra, variables are used to represent unknown values. They act as placeholders for numbers we do not have yet. In this exercise, we used the variable 'y' to represent the number of tickets. When you use a letter like 'y' as a variable, it makes it easy to set up equations and solve problems involving unknown quantities.

Remember, variables can be any letter from the alphabet, such as 'x', 'a', or 'n'. The key is consistency. Once you've chosen a variable, stick with it to avoid confusion.
Linear Equations
A linear equation is an equation that forms a straight line when graphed. It typically has one or more variables raised to the power of 1. In this problem, we create a linear equation to find the total cost of 'y' movie tickets. The linear equation in our case is:

\[ \text{Total Cost} = 13.50y \]

Linear equations are straightforward to solve because they require basic operations like addition, subtraction, multiplication, or division. Understanding linear equations helps you tackle many real-life problems involving proportions and rates.
Basic Multiplication
Multiplication is one of the fundamental arithmetic operations. It involves combining equal groups. In our problem, we multiply the cost of one movie ticket by the number of tickets 'y'. This can be written as:

\[ 13.50 \times y \]

Multiplying by a variable is the same as repeating the value as many times as the variable indicates. Understanding multiplication helps you solve problems quickly and efficiently, especially when dealing with money, distances, and quantities.

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Most popular questions from this chapter

Braving blizzard conditions on the planet Hoth, Luke Skywalker sets out in his snow speeder for a rebel base \(4800 \mathrm{mi}\) away. He travels into a steady headwind and makes the trip in \(3 \mathrm{hr}\). Returning, he finds that the trip back, now with a tailwind, takes only \(2 \mathrm{hr}\). Find the rate of Luke's snow speeder and the wind speed.

Graph each line passing through the given point and having the given slope $$ (0,-2) ; m=-\frac{2}{3} $$

Solve each system by the elimination method. Check each solution. $$ \begin{array}{l} 3 x=3+2 y \\ -\frac{4}{3} x+y=\frac{1}{3} \end{array} $$

A fruit drink is made by mixing juices. Such a drink with \(50 \%\) juice is to be mixed with a drink that is \(30 \%\) juice to obtain \(200 \mathrm{~L}\) of a drink that is \(45 \%\) juice. How much of each should be used?

Solve each system by graphing. If the system is inconsistent or the equations are dependent, say so. \(y=4 x-4\) \(3 x-2 y=3\)
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