Problem 60
Question
In the following exercises, solve each number word problem. Buying in Bulk Alicia bought a package of eight peaches for \(\$ 3.20 .\) Find the cost of each peach.
Step-by-Step Solution
Verified Answer
$0.40 per peach
1Step 1: Understand the Problem
Alicia bought a package of eight peaches for \(\$ 3.20\). We need to find out the cost of each individual peach.
2Step 2: Define Variables
Let \(x\) represent the cost of each peach.
3Step 3: Setup the Equation
Since there are 8 peaches and the total cost is \(\$3.20\), we can write the equation: \[8x = 3.20\] where \(x\) is the cost of one peach.
4Step 4: Solve for x
To find \(x\), divide both sides of the equation by 8: \[x = \frac{3.20}{8}\]
5Step 5: Calculate the Result
Perform the division: \[x = 0.40\]
6Step 6: State the Answer
The cost of each peach is \(\$0.40\).
Key Concepts
solving equationsdivisionvariables
solving equations
When solving number word problems, it's common to set up and solve equations. To find the unknown value, you'll follow logical steps in a sequence. Generally, this involves understanding the problem, defining your variables, creating an equation to model the problem, and then solving for the unknown variable.
In the given problem, Alicia needs to find the price of a single peach when she knows the total cost for eight peaches. By representing the unknown price with a variable (\(x\)), and writing out an equation (\(8x = 3.20\)), she can solve for the cost of one peach. The key steps here include isolating the variable and performing basic algebraic operations like division.
In the given problem, Alicia needs to find the price of a single peach when she knows the total cost for eight peaches. By representing the unknown price with a variable (\(x\)), and writing out an equation (\(8x = 3.20\)), she can solve for the cost of one peach. The key steps here include isolating the variable and performing basic algebraic operations like division.
division
Division is a fundamental arithmetic operation that helps to solve for an unknown part when the total and number of parts are known. In the given problem, you need to find the cost of one peach out of eight, given the total price of 8 peaches is \$3.20.
When you set up the equation \(8x = 3.20\), you can isolate x by dividing both sides of the equation by 8: \(x = \frac{3.20}{8} = 0.40\). Here, division helps to distribute the total cost evenly across all peaches to find the cost per peach.
Remember, performing division accurately is crucial to avoid calculation errors and to reach the correct solution.
When you set up the equation \(8x = 3.20\), you can isolate x by dividing both sides of the equation by 8: \(x = \frac{3.20}{8} = 0.40\). Here, division helps to distribute the total cost evenly across all peaches to find the cost per peach.
Remember, performing division accurately is crucial to avoid calculation errors and to reach the correct solution.
variables
Variables are symbols used to represent unknown values in equations. They allow us to model real-world problems mathematically. In this exercise, the variable \(x\) represents the unknown cost of each peach.
When defining a variable, choose a symbol (often a letter like \(x\), \(y\), or \(z\)) that makes it easy to understand what it stands for. In our problem, we set \(x\) to be the cost of one peach. This helps to keep the equation \(8x = 3.20\) simple and clear.
Once the variable is defined, you can set up the equation based on the problem's conditions, then solve for the variable. In our example, solving \(x = \frac{3.20}{8}\) gives the cost of each peach.
When defining a variable, choose a symbol (often a letter like \(x\), \(y\), or \(z\)) that makes it easy to understand what it stands for. In our problem, we set \(x\) to be the cost of one peach. This helps to keep the equation \(8x = 3.20\) simple and clear.
Once the variable is defined, you can set up the equation based on the problem's conditions, then solve for the variable. In our example, solving \(x = \frac{3.20}{8}\) gives the cost of each peach.
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