Using Ratios to Compare Costs

Oct 13, 2025 by windailys.com 138 views

Introduction

When comparing offers from different banks on checking accounts, it's essential to consider the costs associated with each account. In this article, we will explore how to use ratios, proportions, and percents to compare the costs of checking accounts from two different banks. We will use a real-life scenario to illustrate how to apply these mathematical concepts to make informed decisions.

Understanding the Problem

Kareem is comparing offers from two banks on checking accounts that include debit cards. Bank A charges a $20 monthly fee for a checking account and debit card, while Bank B charges a $15 monthly fee for a checking account and debit card. However, Bank B offers a 10% discount on the monthly fee for customers who maintain a minimum balance of $1,000 in their account. Kareem wants to know which bank offers the better deal.

Using Ratios to Compare Costs

To compare the costs of the two checking accounts, we can use ratios. A ratio is a comparison of two numbers. In this case, we can compare the monthly fees charged by each bank.

Monthly Fee Ratio

Let's calculate the monthly fee ratio for each bank.

Bank A: $20 monthly fee
Bank B: $15 monthly fee (with a 10% discount)

To calculate the monthly fee ratio, we can divide the monthly fee by the minimum balance required to receive the discount.

Bank A: $20 ÷ $0 = ∞ (since there is no minimum balance required)
Bank B: $15 ÷ $1,000 = 0.015 (or 1.5%)

The monthly fee ratio for Bank A is infinite, since there is no minimum balance required to avoid the monthly fee. The monthly fee ratio for Bank B is 1.5%, which means that for every $100 in the account, the customer pays $1.50 in monthly fees.

Using Proportions to Compare Costs

Now that we have the monthly fee ratios, we can use proportions to compare the costs of the two checking accounts. A proportion is a statement that two ratios are equal.

Proportion

Let's set up a proportion to compare the costs of the two checking accounts.

Bank A: $20 monthly fee ÷ $0 minimum balance = ∞
Bank B: $15 monthly fee ÷ $1,000 minimum balance = 0.015

We can set up a proportion to compare the costs of the two checking accounts as follows:

\frac{20}{0} = \frac{15}{1000}

To solve for the unknown, we can cross-multiply:

20 \times 1000 = 15 \times 0

This equation is true, since any number multiplied by 0 is 0. However, we can see that the proportion is not useful in this case, since the monthly fee ratio for Bank A is infinite.

Using Percents to Compare Costs

Now that we have the monthly fee ratios, we can use percents to compare the costs of the two checking accounts. A percent is a way to express a fraction as a decimal.

Percent

Let's calculate the percent of the monthly fee for each bank.

Bank A: $20 monthly fee ÷ $0 minimum balance = ∞ (since there is no minimum balance required)
Bank B: $15 monthly fee ÷ $1,000 minimum balance = 1.5%

The percent of the monthly fee for Bank A is infinite, since there is no minimum balance required to avoid the monthly fee. The percent of the monthly fee for Bank B is 1.5%, which means that for every $100 in the account, the customer pays $1.50 in monthly fees.

Conclusion

In conclusion, we have used ratios, proportions, and percents to compare the costs of two checking accounts from different banks. We have seen that Bank A charges a $20 monthly fee for a checking account and debit card, while Bank B charges a $15 monthly fee for a checking account and debit card, with a 10% discount for customers who maintain a minimum balance of $1,000 in their account. We have calculated the monthly fee ratio, proportion, and percent for each bank, and have seen that Bank B offers the better deal.

Recommendation

Based on our analysis, we recommend that Kareem choose Bank B's checking account, since it offers a lower monthly fee and a 10% discount for customers who maintain a minimum balance of $1,000 in their account.

Future Research

In the future, we plan to explore other mathematical concepts that can be used to compare the costs of checking accounts, such as averages and medians. We also plan to investigate the impact of fees on customer behavior and decision-making.

References

[1] "Ratios and Proportions." Math Open Reference, mathopenref.com/ratios.html.
[2] "Percents." Math Goodies, mathgoodies.com/percent.html.

Appendix

The following is a list of the mathematical concepts used in this article:

Ratios
Proportions
Percents
Averages
Medians

The following is a list of the formulas used in this article:

Ratio: a/b = c/d
Proportion: a/b = c/d
Percent: (a/b) × 100 = c/d

The following is a list of the variables used in this article:

a: monthly fee
b: minimum balance
c: monthly fee ratio
d: minimum balance ratio

Introduction

In our previous article, we explored how to use ratios, proportions, and percents to compare the costs of checking accounts from two different banks. We used a real-life scenario to illustrate how to apply these mathematical concepts to make informed decisions. In this article, we will answer some frequently asked questions (FAQs) related to the topic.

Q&A

Q: What is a ratio?

A: A ratio is a comparison of two numbers. It is a way to express the relationship between two quantities.

Q: How do I calculate a ratio?

A: To calculate a ratio, you simply divide one number by another. For example, if you have a monthly fee of $20 and a minimum balance of $1,000, the ratio would be 20/1000.

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is a way to compare two ratios and determine if they are equal.

Q: How do I calculate a proportion?

A: To calculate a proportion, you simply set up a statement that two ratios are equal. For example, if you have a monthly fee of $20 and a minimum balance of $0, and a monthly fee of $15 and a minimum balance of $1,000, the proportion would be 20/0 = 15/1000.

Q: What is a percent?

A: A percent is a way to express a fraction as a decimal. It is a way to express a part of a whole as a percentage.

Q: How do I calculate a percent?

A: To calculate a percent, you simply multiply a number by a percentage. For example, if you have a monthly fee of $20 and a minimum balance of $1,000, the percent would be (20/1000) × 100 = 2%.

Q: How do I use ratios, proportions, and percents to compare the costs of checking accounts?

A: To compare the costs of checking accounts, you can use ratios, proportions, and percents to determine which account offers the best deal. For example, if you have a monthly fee of $20 and a minimum balance of $0, and a monthly fee of $15 and a minimum balance of $1,000, you can use ratios, proportions, and percents to determine which account offers the best deal.

Q: What are some common mistakes to avoid when using ratios, proportions, and percents?

A: Some common mistakes to avoid when using ratios, proportions, and percents include:

Not considering the minimum balance required to avoid fees
Not calculating the ratio, proportion, or percent correctly
Not comparing the costs of different accounts
Not considering the impact of fees on customer behavior and decision-making

Q: What are some real-life applications of ratios, proportions, and percents?

A: Some real-life applications of ratios, proportions, and percents include:

Comparing the costs of different checking accounts
Determining the best deal on a credit card
Calculating the interest rate on a loan
Comparing the costs of different insurance policies

Q: How can I practice using ratios, proportions, and percents?

A: You can practice using ratios, proportions, and percents by:

Using online calculators to calculate ratios, proportions, and percents
Practicing with sample problems
Using real-life scenarios to apply ratios, proportions, and percents
Joining a study group or seeking help from a tutor

Conclusion

In conclusion, ratios, proportions, and percents are essential mathematical concepts that can be used to compare the costs of checking accounts. By understanding how to use these concepts, you can make informed decisions and choose the best account for your needs. We hope this Q&A article has been helpful in answering your questions and providing you with a better understanding of ratios, proportions, and percents.