The Grocery Store Sells Kumquats For $ 5.00 \$5.00 $5.00 A Pound And Asian Pears For $ 3.25 \$3.25 $3.25 A Pound. Write An Equation In Standard Form For The Weights Of Kumquats K K K And Asian Pears P P P That A Customer Could Buy With

Introduction

In this article, we will delve into the world of mathematics and explore a real-world problem involving the purchase of kumquats and Asian pears at a grocery store. The problem is as follows: a customer wants to buy kumquats and Asian pears with a total cost of $\$8.00$. The store sells kumquats for $\$5.00$ a pound and Asian pears for $\$3.25$ a pound. We will write an equation in standard form to represent the weights of kumquats $k$ and Asian pears $p$ that the customer could buy with $\$8.00$.

The Problem

Let's denote the weight of kumquats as $k$ pounds and the weight of Asian pears as $p$ pounds. The cost of kumquats is $\$5.00$ per pound, and the cost of Asian pears is $\$3.25$ per pound. The customer wants to spend a total of $\$8.00$ on kumquats and Asian pears. We can write an equation to represent this situation:

$$5k + 3.25p = 8$$

This equation states that the total cost of kumquats ($5k$) plus the total cost of Asian pears ($3.25p$) is equal to the total amount the customer wants to spend ($8$).

Standard Form

To write the equation in standard form, we need to isolate the variables $k$ and $p$ on one side of the equation. We can do this by subtracting $3.25p$ from both sides of the equation:

$$5k = 8 - 3.25p$$

Next, we can divide both sides of the equation by $5$ to solve for $k$:

$$k = \frac{8 - 3.25p}{5}$$

This is the equation in standard form, where $k$ is the weight of kumquats and $p$ is the weight of Asian pears.

Graphical Representation

We can also represent this equation graphically by plotting the lines $y = \frac{8 - 3.25x}{5}$ and $y = 0$ on a coordinate plane. The line $y = \frac{8 - 3.25x}{5}$ represents the equation in standard form, and the line $y = 0$ represents the x-axis.

Solving for $k$ and $p$

To find the values of $k$ and $p$ that satisfy the equation, we can substitute different values of $p$ into the equation and solve for $k$. For example, if we let $p = 0$, we get:

$$k = \frac{8 - 3.25(0)}{5} = \frac{8}{5} = 1.6$$

This means that if the customer buys no Asian pears ($p = 0$), they can buy $1.6$ pounds of kumquats ($k = 1.6$).

Conclusion

In this article, we explored a real-world problem involving the purchase of kumquats and Asian pears at a grocery store. We wrote an equation in standard form to represent the weights of kumquats $k$ and Asian pears $p$ that the customer could buy with $\$8.00$. We also represented the equation graphically and solved for $k$ and $p$ using different values of $p$. This problem demonstrates the importance of mathematical modeling in real-world applications.

References

• [1] "Mathematics for the Nonmathematician" by Morris Kline
• [2] "Calculus" by Michael Spivak
• [3] "Linear Algebra and Its Applications" by Gilbert Strang

Further Reading

• [1] "Mathematical Modeling" by James R. Schott
• [2] "Applied Mathematics" by Richard Haberman
• [3] "Mathematics for Engineers and Scientists" by Donald R. Hill

Glossary

• Kumquats: a type of fruit that is typically sold by the pound
• Asian pears: a type of fruit that is typically sold by the pound
• Standard form: a mathematical representation of an equation where the variables are isolated on one side of the equation
• Graphical representation: a visual representation of an equation using a coordinate plane
• Solving for $k$ and $p$: finding the values of $k$ and $p$ that satisfy the equation
  The Kumquat and Asian Pear Problem: A Q&A Article =====================================================

Introduction

In our previous article, we explored a real-world problem involving the purchase of kumquats and Asian pears at a grocery store. We wrote an equation in standard form to represent the weights of kumquats $k$ and Asian pears $p$ that the customer could buy with $\$8.00$. In this article, we will answer some frequently asked questions about the problem and provide additional insights.

Q: What is the cost of kumquats and Asian pears per pound?

A: The cost of kumquats is $\$5.00$ per pound, and the cost of Asian pears is $\$3.25$ per pound.

Q: What is the total amount the customer wants to spend on kumquats and Asian pears?

A: The customer wants to spend a total of $\$8.00$ on kumquats and Asian pears.

Q: How can we represent the weights of kumquats $k$ and Asian pears $p$ that the customer could buy with $\$8.00$?

A: We can write an equation to represent this situation:

$$5k + 3.25p = 8$$

This equation states that the total cost of kumquats ($5k$) plus the total cost of Asian pears ($3.25p$) is equal to the total amount the customer wants to spend ($8$).

Q: How can we solve for $k$ and $p$?

A: We can solve for $k$ and $p$ by substituting different values of $p$ into the equation and solving for $k$. For example, if we let $p = 0$, we get:

$$k = \frac{8 - 3.25(0)}{5} = \frac{8}{5} = 1.6$$

This means that if the customer buys no Asian pears ($p = 0$), they can buy $1.6$ pounds of kumquats ($k = 1.6$).

Q: What is the graphical representation of the equation?

A: We can represent the equation graphically by plotting the lines $y = \frac{8 - 3.25x}{5}$ and $y = 0$ on a coordinate plane. The line $y = \frac{8 - 3.25x}{5}$ represents the equation in standard form, and the line $y = 0$ represents the x-axis.

Q: What are some real-world applications of this problem?

A: This problem has many real-world applications, such as:

• Grocery shopping: This problem can be used to model the cost of buying different types of fruits and vegetables at a grocery store.
• Financial planning: This problem can be used to model the cost of buying different types of investments, such as stocks and bonds.
• Supply and demand: This problem can be used to model the supply and demand of different types of goods and services.

Q: What are some tips for solving this problem?

A: Here are some tips for solving this problem:

• Read the problem carefully: Make sure you understand what the problem is asking for.
• Write an equation: Write an equation to represent the problem.
• Solve for the variables: Solve for the variables $k$ and $p$ by substituting different values of $p$ into the equation and solving for $k$.
• Graph the equation: Graph the equation to visualize the solution.

Conclusion

In this article, we answered some frequently asked questions about the kumquat and Asian pear problem and provided additional insights. We also discussed some real-world applications of the problem and provided tips for solving it. We hope this article has been helpful in understanding the problem and its solutions.