Use a variable for the unknown quantity

Oct 13, 2025 by talynt.org 132 views

If 19 Candy Bars Cost $28.88, How Much Do 12 Candy Bars Cost?

Understanding the Problem

When faced with a problem involving proportions, it's essential to identify the given information and the unknown quantity. In this scenario, we're given the cost of 19 candy bars, which is $28.88. We need to find the cost of 12 candy bars.

Step 1: Record the Proportion

To solve this problem, we'll use a proportion to relate the given information to the unknown quantity. A proportion is a statement that two ratios are equal. In this case, the proportion will be:

19 candy bars / $28.88 = 12 candy bars / x

where x is the unknown quantity, which represents the cost of 12 candy bars.

Step 2: Solve the Proportion

To solve the proportion, we can use cross-multiplication, which involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. This will give us an equation that we can solve for x.

19x = 12 * $28.88

19x = $346.56

x = $346.56 / 19

x = $18.22

Therefore, the cost of 12 candy bars is $18.22.

Discussion

This problem involves using proportions to solve a real-world scenario. Proportions are a fundamental concept in mathematics, and they have numerous applications in various fields, such as finance, engineering, and science. In this case, the proportion helps us to find the cost of 12 candy bars based on the given information.

Real-World Applications

Proportions have many real-world applications, including:

Finance: Proportions are used to calculate interest rates, investment returns, and other financial metrics.
Engineering: Proportions are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Science: Proportions are used to describe the relationships between variables in scientific experiments and models.

Conclusion

In conclusion, using proportions to solve problems is a powerful tool in mathematics. By identifying the given information and the unknown quantity, we can set up a proportion and solve for the unknown quantity. This problem demonstrates how proportions can be used to solve real-world scenarios, and it highlights the importance of proportions in various fields.

Additional Examples

Here are a few additional examples of how proportions can be used to solve problems:

Example 1: If 5 pounds of coffee cost $15, how much does 2 pounds of coffee cost?
Example 2: If 8 hours of labor cost $40, how much does 4 hours of labor cost?
Example 3: If 12 ounces of juice cost $3, how much does 6 ounces of juice cost?

These examples demonstrate how proportions can be used to solve a variety of problems, from finance to science.

Tips and Tricks

Here are a few tips and tricks for working with proportions:

Use a variable for the unknown quantity: This will help you to set up the proportion and solve for the unknown quantity.
Use cross-multiplication: This will help you to solve the proportion and find the unknown quantity.
Check your units: Make sure that the units are consistent throughout the problem.
Use a calculator: If necessary, use a calculator to check your calculations and find the unknown quantity.

By following these tips and tricks, you can become more confident and proficient in working with proportions.
Frequently Asked Questions (FAQs) About Proportions

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is a way of expressing a relationship between two quantities.

Q: How do I set up a proportion?

A: To set up a proportion, you need to identify the given information and the unknown quantity. You can then write a statement that relates the two quantities, using a colon or an equal sign.

Q: What is the difference between a proportion and a ratio?

A: A ratio is a comparison of two quantities, while a proportion is a statement that two ratios are equal. For example, 2:3 is a ratio, while 2:3 = 4:6 is a proportion.

Q: How do I solve a proportion?

A: To solve a proportion, you can use cross-multiplication, which involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. This will give you an equation that you can solve for the unknown quantity.

Q: What are some real-world applications of proportions?

A: Proportions have many real-world applications, including finance, engineering, and science. They are used to calculate interest rates, investment returns, and other financial metrics, as well as to design and optimize systems.

Q: How do I check my work when solving a proportion?

A: To check your work, make sure that the units are consistent throughout the problem, and that the equation is balanced. You can also use a calculator to check your calculations and find the unknown quantity.

Q: What are some common mistakes to avoid when working with proportions?

A: Some common mistakes to avoid when working with proportions include:

Not using a variable for the unknown quantity: This can make it difficult to set up the proportion and solve for the unknown quantity.
Not using cross-multiplication: This can make it difficult to solve the proportion and find the unknown quantity.
Not checking units: This can lead to incorrect calculations and results.
Not using a calculator: This can make it difficult to check calculations and find the unknown quantity.

Q: How can I practice working with proportions?

A: You can practice working with proportions by:

Solving problems: Try solving problems that involve proportions, such as those found in math textbooks or online resources.
Using online resources: There are many online resources available that can help you practice working with proportions, including video tutorials and interactive exercises.
Working with a tutor: If you are having trouble understanding proportions, consider working with a tutor who can provide one-on-one instruction and support.

Q: What are some advanced topics related to proportions?

A: Some advanced topics related to proportions include:

Similar triangles: This involves using proportions to solve problems involving similar triangles.
Similar figures: This involves using proportions to solve problems involving similar figures.
Percentages: This involves using proportions to solve problems involving percentages.
Fractions: This involves using proportions to solve problems involving fractions.

By understanding these advanced topics, you can become more proficient and confident in working with proportions.

Q: How can I apply proportions to real-world problems?

A: You can apply proportions to real-world problems by:

Identifying the given information: This involves identifying the quantities that are given in the problem.
Identifying the unknown quantity: This involves identifying the quantity that you need to find.
Setting up the proportion: This involves writing a statement that relates the two quantities.
Solving the proportion: This involves using cross-multiplication to solve for the unknown quantity.

By following these steps, you can apply proportions to real-world problems and find solutions to complex problems.