Lisa Has $ 7.80 \$7.80 $7.80 To Spend On Some Tomatoes And A Loaf Of Bread. Tomatoes Cost $ 1.20 \$1.20 $1.20 Per Pound, And A Loaf Of Bread Costs $ 1.80 \$1.80 $1.80 .The Inequality 1.20 X + 1.80 ≤ 7.80 1.20x + 1.80 \leq 7.80 1.20 X + 1.80 ≤ 7.80 Models This Situation, Where X X X

Mar 10, 2025 by ADMIN 283 views

Solving Inequalities: A Real-World Problem

In this article, we will explore a real-world problem that involves solving an inequality. The problem is as follows: Lisa has $\$7.80$ to spend on some tomatoes and a loaf of bread. Tomatoes cost $\$1.20$ per pound, and a loaf of bread costs $\$1.80$ . We will use the inequality $1.20x + 1.80 \leq 7.80$ to model this situation, where $x$ represents the number of pounds of tomatoes Lisa can buy.

To solve this problem, we need to understand the given information and the inequality that models the situation. The inequality $1.20x + 1.80 \leq 7.80$ represents the total cost of the tomatoes and the bread, which cannot exceed $\$7.80$ . The variable $x$ represents the number of pounds of tomatoes that Lisa can buy.

To solve the inequality, we need to isolate the variable $x$ . We can do this by subtracting $1.80$ from both sides of the inequality:

1.20x + 1.80 - 1.80 \leq 7.80 - 1.80

This simplifies to:

1.20x \leq 6.00

Next, we can divide both sides of the inequality by $1.20$ to solve for $x$ :

\frac{1.20x}{1.20} \leq \frac{6.00}{1.20}

This simplifies to:

x \leq 5.00

The solution to the inequality, $x \leq 5.00$ , tells us that Lisa can buy at most 5 pounds of tomatoes with her $\$7.80$ . This means that if Lisa buys 5 pounds of tomatoes, she will have exactly $\$7.80$ left over to buy the loaf of bread.

To check our solution, we can plug in $x = 5$ into the original inequality:

1.20(5) + 1.80 \leq 7.80

This simplifies to:

6.00 + 1.80 \leq 7.80

Which is true, since $7.80 \leq 7.80$ . This confirms that our solution is correct.

In this article, we solved a real-world problem involving an inequality. We used the inequality $1.20x + 1.80 \leq 7.80$ to model the situation, where $x$ represents the number of pounds of tomatoes Lisa can buy. We solved the inequality by isolating the variable $x$ and found that Lisa can buy at most 5 pounds of tomatoes with her $\$7.80$ . We also checked our solution to confirm that it is correct.

Solving inequalities is an important skill in mathematics, and it has many real-world applications. In this article, we saw how solving an inequality can be used to model a real-world problem involving budgeting and shopping. Other real-world applications of solving inequalities include:

Finance: Solving inequalities can be used to model financial situations, such as calculating interest rates or determining the minimum amount of money needed to save for a goal.
Science: Solving inequalities can be used to model scientific situations, such as calculating the rate of change of a quantity or determining the minimum amount of a substance needed to achieve a certain effect.
Engineering: Solving inequalities can be used to model engineering situations, such as calculating the stress on a material or determining the minimum amount of energy needed to power a device.

Here are some tips and tricks for solving inequalities:

Read the problem carefully: Make sure you understand what the problem is asking and what information is given.
Use inverse operations: Use inverse operations, such as addition and subtraction, to isolate the variable.
Check your solution: Plug your solution back into the original inequality to confirm that it is correct.

In conclusion, solving inequalities is an important skill in mathematics that has many real-world applications. In this article, we solved a real-world problem involving an inequality and saw how it can be used to model a situation involving budgeting and shopping. We also discussed some tips and tricks for solving inequalities and provided some examples of real-world applications.
Solving Inequalities: A Real-World Problem - Q&A

In our previous article, we explored a real-world problem that involved solving an inequality. We used the inequality $1.20x + 1.80 \leq 7.80$ to model the situation, where $x$ represents the number of pounds of tomatoes Lisa can buy. In this article, we will answer some common questions that people may have when solving inequalities.

Q: What is an inequality?

A: An inequality is a mathematical statement that compares two expressions using a symbol such as <, >, ≤, or ≥. Inequalities can be used to model real-world situations, such as budgeting and shopping.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality sign. You can do this by using inverse operations, such as addition and subtraction, to get the variable by itself.

Q: What is the difference between an inequality and an equation?

A: An equation is a mathematical statement that states that two expressions are equal. An inequality, on the other hand, states that two expressions are not equal, but are related in some way.

Q: How do I check my solution to an inequality?

A: To check your solution to an inequality, you need to plug your solution back into the original inequality and see if it is true. If it is true, then your solution is correct.

Q: What are some common mistakes to avoid when solving inequalities?

A: Some common mistakes to avoid when solving inequalities include:

Not reading the problem carefully: Make sure you understand what the problem is asking and what information is given.
Not using inverse operations: Use inverse operations, such as addition and subtraction, to isolate the variable.
Not checking your solution: Plug your solution back into the original inequality to confirm that it is correct.

Q: How do I use inequalities in real-world situations?

A: Inequalities can be used to model real-world situations, such as budgeting and shopping. For example, if you have a budget of $\$100$ and you want to buy a shirt that costs $\$50$ , you can use an inequality to determine how much money you have left over.

Q: What are some examples of real-world applications of inequalities?

A: Some examples of real-world applications of inequalities include:

Finance: Solving inequalities can be used to model financial situations, such as calculating interest rates or determining the minimum amount of money needed to save for a goal.
Science: Solving inequalities can be used to model scientific situations, such as calculating the rate of change of a quantity or determining the minimum amount of a substance needed to achieve a certain effect.
Engineering: Solving inequalities can be used to model engineering situations, such as calculating the stress on a material or determining the minimum amount of energy needed to power a device.

In conclusion, solving inequalities is an important skill in mathematics that has many real-world applications. In this article, we answered some common questions that people may have when solving inequalities and provided some examples of real-world applications. We hope that this article has been helpful in understanding how to solve inequalities and how to use them in real-world situations.

Here are some tips and tricks for solving inequalities:

Read the problem carefully: Make sure you understand what the problem is asking and what information is given.
Use inverse operations: Use inverse operations, such as addition and subtraction, to isolate the variable.
Check your solution: Plug your solution back into the original inequality to confirm that it is correct.

Solving inequalities has many real-world applications, including:

Finance: Solving inequalities can be used to model financial situations, such as calculating interest rates or determining the minimum amount of money needed to save for a goal.
Science: Solving inequalities can be used to model scientific situations, such as calculating the rate of change of a quantity or determining the minimum amount of a substance needed to achieve a certain effect.
Engineering: Solving inequalities can be used to model engineering situations, such as calculating the stress on a material or determining the minimum amount of energy needed to power a device.