Finding the Total Cost of the Bike

Oct 13, 2025 by talynt.org 2 views

Introduction

In this problem, we are given that Sam's parents agreed to pay 25 percent of the cost of a new bike if Sam paid the rest. We need to find out how much Sam has to pay for the bike. To solve this problem, we will use the concept of percentages and proportions.

Understanding Percentages

Percentages are a way of expressing a part of a whole as a fraction of 100. In this case, 25 percent means that Sam's parents will pay 25/100 or 1/4 of the cost of the bike. The remaining 75 percent will be paid by Sam.

Setting Up the Problem

Let's assume that the total cost of the bike is x dollars. Since Sam's parents will pay 25 percent of the cost, they will pay 0.25x dollars. The remaining 75 percent will be paid by Sam, which is 0.75x dollars.

Finding the Total Cost of the Bike

We are given that Sam's parents agreed to pay 65 dollars for their part of the bike. This means that 0.25x = 65. We can solve for x by dividing both sides by 0.25.

x = 65 / 0.25
x = 260

So, the total cost of the bike is 260 dollars.

Calculating Sam's Share of the Cost

Now that we know the total cost of the bike, we can calculate Sam's share of the cost. Since Sam's parents will pay 25 percent of the cost, Sam will pay the remaining 75 percent. We can calculate Sam's share by multiplying the total cost by 0.75.

sam_share = 0.75 * 260
sam_share = 195

So, Sam will pay 195 dollars for his part of the bike.

Conclusion

In this problem, we used the concept of percentages and proportions to find out how much Sam has to pay for a new bike. We assumed that the total cost of the bike is x dollars and that Sam's parents will pay 25 percent of the cost. We then calculated Sam's share of the cost by multiplying the total cost by 0.75. We found that Sam will pay 195 dollars for his part of the bike.

Discussion

This problem is a great example of how percentages can be used to express a part of a whole. It also shows how proportions can be used to solve problems involving percentages. In real-life situations, percentages are used to express discounts, interest rates, and other types of proportions.

Example Use Cases

Discounts: When shopping online, you may see discounts expressed as percentages. For example, a 20 percent discount on a 100 dollar item would be 20 dollars off.
Interest Rates: When borrowing money, you may be charged interest rates expressed as percentages. For example, a 5 percent interest rate on a 1000 dollar loan would be 50 dollars per year.
Proportions: When solving problems involving proportions, you may need to use percentages to express the parts of a whole. For example, if you have a recipe that calls for 25 percent sugar and 75 percent flour, you would need to use percentages to express the proportions of each ingredient.

Tips and Tricks

Use a calculator: When working with percentages, it's easy to make mistakes. Use a calculator to ensure that your calculations are accurate.
Check your units: When working with percentages, make sure that your units are consistent. For example, if you're working with dollars, make sure that your percentages are expressed as decimals.
Use proportions: When solving problems involving proportions, use percentages to express the parts of a whole. This will make it easier to solve the problem and ensure that your answer is accurate.

Conclusion

Q: What is a percentage?

A: A percentage is a way of expressing a part of a whole as a fraction of 100. It is a ratio of a part to a whole, expressed as a decimal or a fraction.

Q: How do I calculate a percentage?

A: To calculate a percentage, you need to divide the part by the whole and multiply by 100. For example, if you want to calculate 25 percent of 100, you would divide 25 by 100 and multiply by 100, which equals 25.

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 use proportions to solve problems?

A: To use proportions to solve problems, you need to set up a proportion and then solve for the unknown quantity. For example, if you have a recipe that calls for 25 percent sugar and 75 percent flour, you would set up a proportion to find the amount of sugar and flour needed.

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

A: A percentage is a way of expressing a part of a whole as a fraction of 100, while a proportion is a statement that two ratios are equal. While percentages are used to express parts of a whole, proportions are used to express relationships between two quantities.

Q: How do I use percentages to solve problems involving discounts?

A: To use percentages to solve problems involving discounts, you need to calculate the discount amount by multiplying the original price by the discount percentage. For example, if you want to calculate a 20 percent discount on a 100 dollar item, you would multiply 100 by 0.20, which equals 20.

Q: How do I use percentages to solve problems involving interest rates?

A: To use percentages to solve problems involving interest rates, you need to calculate the interest amount by multiplying the principal amount by the interest rate. For example, if you want to calculate a 5 percent interest rate on a 1000 dollar loan, you would multiply 1000 by 0.05, which equals 50.

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

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

Not checking units
Not using a calculator
Not setting up proportions correctly
Not solving for the unknown quantity

Q: How can I practice using percentages and proportions to solve problems?

A: You can practice using percentages and proportions to solve problems by working through examples and exercises. You can also use online resources and calculators to help you practice and check your work.

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

A: Some real-world applications of percentages and proportions include:

Discounts and sales
Interest rates and loans
Recipes and cooking
Science and engineering
Finance and economics

Conclusion

In conclusion, percentages and proportions are important concepts in mathematics that are used to express parts of a whole and relationships between two quantities. By understanding how to use percentages and proportions, you can solve a wide range of problems involving discounts, interest rates, and other types of proportions.