A Lotion Is Made From An Oil Blend Costing $ 1.50 \$1.50 $1.50 Per Ounce And Glycerin Costing $ 1.00 \$1.00 $1.00 Per Ounce. Four Ounces Of Lotion Costs $ 5.50 \$5.50 $5.50 .Which Value Could Replace X X X On The Table?A. ( 4 − G ) × 1.5 (4-g) \times 1.5 ( 4 − G ) × 1.5

Introduction

In this article, we will delve into the world of mathematics and explore a real-world scenario involving the production of a lotion. The lotion is made from a blend of oil and glycerin, with the oil costing $\$1.50$ per ounce and the glycerin costing $\$1.00$ per ounce. We are given that four ounces of lotion costs $\$5.50$. Our task is to determine which value could replace $x$ on the table.

The Problem

Let's break down the problem and understand what is being asked. We have two ingredients: oil and glycerin. The oil costs $\$1.50$ per ounce, and the glycerin costs $\$1.00$ per ounce. We are given that four ounces of lotion costs $\$5.50$. This means that the total cost of the oil and glycerin in four ounces of lotion is $\$5.50$.

The Equation

Let's denote the number of ounces of oil used as $x$. Since the oil costs $\$1.50$ per ounce, the total cost of the oil used is $1.5x$. The number of ounces of glycerin used is $4-x$, since we have four ounces of lotion in total. The glycerin costs $\$1.00$ per ounce, so the total cost of the glycerin used is $1(4-x) = 4-x$.

The Total Cost

The total cost of the oil and glycerin used is the sum of their individual costs. Therefore, the total cost is $1.5x + (4-x)$. We are given that this total cost is equal to $\$5.50$. So, we can set up the equation:

$$1.5x + (4-x) = 5.50$$

Solving the Equation

To solve for $x$, we need to simplify the equation. Let's start by combining like terms:

$$1.5x + 4 - x = 5.50$$

$$0.5x + 4 = 5.50$$

Next, let's subtract 4 from both sides of the equation:

$$0.5x = 1.50$$

Finally, let's divide both sides of the equation by 0.5:

$$x = 3$$

Conclusion

Therefore, the value that could replace $x$ on the table is 3.

Discussion

The problem presented in this article is a classic example of a linear equation. The equation $1.5x + (4-x) = 5.50$ represents the total cost of the oil and glycerin used in four ounces of lotion. By solving for $x$, we can determine the number of ounces of oil used. In this case, the value of $x$ is 3, which means that 3 ounces of oil are used in four ounces of lotion.

Mathematical Concepts

This problem involves several mathematical concepts, including:

• Linear equations: The equation $1.5x + (4-x) = 5.50$ is a linear equation, which means that it can be represented graphically as a straight line.
• Variables: The variable $x$ represents the number of ounces of oil used.
• Constants: The constants 1.5 and 4 represent the cost of the oil and the total number of ounces of lotion, respectively.
• Operations: The operations of addition, subtraction, multiplication, and division are used to simplify the equation and solve for $x$.

Real-World Applications

This problem has several real-world applications, including:

• Manufacturing: The problem can be used to determine the cost of production of a lotion, which is an important consideration for manufacturers.
• Business: The problem can be used to determine the profit margin of a lotion, which is an important consideration for businesses.
• Science: The problem can be used to determine the concentration of a solution, which is an important consideration in scientific applications.

Conclusion

In conclusion, the problem presented in this article is a classic example of a linear equation. By solving for $x$, we can determine the number of ounces of oil used in four ounces of lotion. The value of $x$ is 3, which means that 3 ounces of oil are used in four ounces of lotion. This problem has several real-world applications, including manufacturing, business, and science.

Introduction

In our previous article, we delved into the world of mathematics and explored a real-world scenario involving the production of a lotion. The lotion is made from a blend of oil and glycerin, with the oil costing $\$1.50$ per ounce and the glycerin costing $\$1.00$ per ounce. We were given that four ounces of lotion costs $\$5.50$. Our task was to determine which value could replace $x$ on the table.

Q&A

Q: What is the cost of the oil used in four ounces of lotion?

A: The cost of the oil used is $1.5x$, where $x$ is the number of ounces of oil used.

Q: What is the cost of the glycerin used in four ounces of lotion?

A: The cost of the glycerin used is $1(4-x) = 4-x$, where $x$ is the number of ounces of oil used.

Q: What is the total cost of the oil and glycerin used in four ounces of lotion?

A: The total cost is $1.5x + (4-x) = 5.50$.

Q: How do we solve for $x$ in the equation $1.5x + (4-x) = 5.50$?

A: To solve for $x$, we need to simplify the equation by combining like terms, subtracting 4 from both sides, and then dividing both sides by 0.5.

Q: What is the value of $x$ that solves the equation $1.5x + (4-x) = 5.50$?

A: The value of $x$ that solves the equation is 3.

Q: What does the value of $x$ represent in the context of the problem?

A: The value of $x$ represents the number of ounces of oil used in four ounces of lotion.

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

A: Some real-world applications of this problem include manufacturing, business, and science.

Q: How can this problem be used in a manufacturing setting?

A: This problem can be used to determine the cost of production of a lotion, which is an important consideration for manufacturers.

Q: How can this problem be used in a business setting?

A: This problem can be used to determine the profit margin of a lotion, which is an important consideration for businesses.

Q: How can this problem be used in a scientific setting?

A: This problem can be used to determine the concentration of a solution, which is an important consideration in scientific applications.

Conclusion

In conclusion, the problem presented in this article is a classic example of a linear equation. By solving for $x$, we can determine the number of ounces of oil used in four ounces of lotion. The value of $x$ is 3, which means that 3 ounces of oil are used in four ounces of lotion. This problem has several real-world applications, including manufacturing, business, and science.

Frequently Asked Questions

Q: What is the cost of the oil used in four ounces of lotion if the value of $x$ is 3?

A: The cost of the oil used is $1.5(3) = 4.50$.

Q: What is the cost of the glycerin used in four ounces of lotion if the value of $x$ is 3?

A: The cost of the glycerin used is $1(4-3) = 1.00$.

Q: What is the total cost of the oil and glycerin used in four ounces of lotion if the value of $x$ is 3?

A: The total cost is $4.50 + 1.00 = 5.50$.

Additional Resources

• For more information on linear equations, please see our article on Linear Equations.
• For more information on real-world applications of mathematics, please see our article on Real-World Applications of Mathematics.

Conclusion

In conclusion, the problem presented in this article is a classic example of a linear equation. By solving for $x$, we can determine the number of ounces of oil used in four ounces of lotion. The value of $x$ is 3, which means that 3 ounces of oil are used in four ounces of lotion. This problem has several real-world applications, including manufacturing, business, and science.