Solving Percent Problems to Prepare for College

Finding percent problems tricky? You’re not alone. Our guide walks you through the entire process from start to finish, so you’ll become an expert in no time.

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As a high school student applying to college, demonstrating strong skills in math on admissions tests, like the SAT, is extremely important. Solving percent problems, an area that confuses many students, is essential for many courses, such as AP Calculus. 

Mastering concepts like finding percentages of numbers, determining percent differences between amounts, and figuring out the original whole given a percentage part will help you conquer these questions on test day and beyond.

This article explains the basics of working with percentages from beginner to advanced skill levels. You’ll get step-by-step examples tailored to common scenarios high schoolers encounter, from calculating tips to figuring out sale prices. With these helpful math formulas and practice, you can become a percent problem pro!

Finding a Percent of a Number

To figure out how to find a percent of a number, divide the number by the total and multiply the result by 100. Whether you’re saving up money from your summer job, calculating tips, or determining sale prices, knowing how to find percentages of amounts provides useful quantitative data.

For example, maybe you need to calculate 15% of the money you earned babysitting to put into your savings account. Or perhaps you want to estimate how much you’ll need to tip on top of a restaurant bill.

Finding a percent of a number is straightforward once you know the steps:

1. Convert the percentage to a decimal: Divide the percentage by 100. For example, 10% becomes 0.10, and 15% becomes 0.15.
2. Multiply the decimal by the total amount: The decimal percentage acts as a multiplier you can use to calculate what proportion of the total number you want.

Let’s walk through an example. Say you earn $100 babysitting over the summer and want to put 15% of that into your savings account.

• You earned $100 total babysitting
• 15% of $100 can be represented as 0.15
• 0.15 * $100 = $15
• So you would put $15 into your savings

See? Converting percentages to decimals and then multiplying gives you an exact portion of any total number.

Let's practice with a few more examples relevant to high schoolers:

As you can see, finding a percentage of a number is fairly straightforward once you know the math involved. Converting percentages to decimals and multiplying makes solving these problems a breeze!

Finding the Percent Between Two Numbers

To find the percent between two numbers, find the average of the two numbers and divide the difference by the average. Multiply the result by 100 to express the percentage. 

This could come in handy for figuring out your percent score of 85 out of 100 points on a test. Or perhaps you’re comparing the number of college acceptance letters you received to the total number you were waiting to hear back from.

Let’s try out an example of unknown percentage problem-solving:

Say you received seven college acceptance letters out of 20 schools you applied to. What percent of schools said yes?

• Given facts:some text
  • You got into seven schools out of 20 total
  • 7/20 simplifies to 7/20 or 0.35
  • Move the decimal point two spots to the right: 35%

Therefore, 35% of the schools you applied to accepted you.

Here are some more situations where you'd calculate an unknown percentage:

Figuring out an unknown percentage is extremely handy for gauging spending, savings, test performance, and more. Understanding how to solve these percent problems will prepare you for the real world!

Finding the Whole Given a Percent

To find the original whole given a percent:

1. Multiply the part by 100 and divide by the percent.
2. This gives you the total original number.

This can come in handy if, for example, you saved 15% of your summer job earnings, and you want to know how much you originally made. This process is very similar to finding a percentage of a number, only backward!

Let's try an example of a whole given a percent problem:

If you saved $126, which was 15% of your summer job earnings, how much did you originally make?

• You saved $126, which was 15% of your total summer earnings
• Convert 15% to 0.15
• $126 / 0.15 = $840
• Therefore, if saving $126 was 15% of your summer earnings, your total earnings must have been $840

Now let's practice:

While finding the original whole from a percentage takes an extra step, the same concepts apply. Converting percentages, dividing, and multiplying allows you to work backward from a percent amount to the total number.

Tips for Solving More Complex Percent Problems

You’ve mastered the basics—finding percentages of numbers, determining unknown percentages between amounts, and calculating wholes from percentages. Now it’s time to level up your skills to master multi-step percent problem-solving.

When word problems involve multiple percentages taken at different times, various unknowns, and real-world scenarios like discounts upon discounts, it’s easy to get overwhelmed. Luckily, there are straightforward techniques you can apply to break down and solve even the most convoluted percent questions.

1. Carefully Read the Entire Problem

Before blindly jumping into calculations when facing a wordy percent problem, first carefully read the entire question from start to finish. Key details could be buried in the middle or end that provide clues on how to proceed. 

Highlight or underline numbers and variables you know as well as what the actual unknown is that you need to solve for. Having a clear picture sets you up for success.

2. Break It Down Step-By-Step

Now that you’ve identified the key components of the complex question, break it down into logical steps. Write out what needs to happen first, second, etc., to ultimately get to the solution.

Let’s follow this example:

A clothing store is having a sale. They first discount the original price by 30%. After applying the 30% discount, they take an additional 15% off the newly discounted price. If the original price of a jacket was $100, what would be the final price after applying both discounts?

Follow these steps to solve complex multi-step problems like this one:

1. Take 30% of the original price
2. Subtract this discount
3. New discounted price
4. Take 15% of the discounted price
5. Subtract this amount to get the final price

Thinking through the precise order of operations helps you systematically work through multi-layered problems.

3. Start Simple

If a problem still seems confusing after breaking it down, try substituting simpler numbers to walk through a basic version. For example, instead of a sweater originally $100, try an item originally $10 instead. Or instead of 40% off, use 10% off. 

Going through rounds with clean hypothetical numbers provides a clearer picture of what mathematical operations and sequence of steps will lead to the solution. The process needed often clicks better when practiced in initial straightforward cases.

4. Double-Check Your Work

Especially on longer, multi-step problems, it’s important to double-check that your final number makes logical sense given the question’s parameters. 

For example, if you solved for a total discounted price after several rounds of percent-off coupons, does the final number seem reasonable? Is it at least smaller than the original pre-discount amount? 

Scanning back through to confirm you applied discounts properly and didn’t mix up any minus signs prevents careless errors.

Let's apply these strategies to some more advanced questions:

These examples reinforce having a logical process to break down more complex questions. Applying targeted percent strategies step-by-step helps you solve these problems with ease!

Why Mastering Percents Matters for College

If you’ll be taking standardized tests like the SAT or ACT for college admission, mastering percent problems is a must for college. The SAT Math section contains multiple questions involving percentages that test your ability to calculate, estimate, and analyze percentages and percent changes.

The reading comprehension section also often includes topics related to business, social sciences, and real-life scenarios where you’ll need to interpret percentages to answer questions correctly.

Beyond tests, understanding how to solve percent problems will prove invaluable no matter what you study in college. Majors like business, accounting, finance, economics, social sciences, health sciences, and more rely heavily on percentages. 

Let the example questions and step-by-step strategies in this article equip you to conquer percentages with confidence - both for college admissions and academic success!

If you’re still struggling with percent problems, consider booking a session with a professional tutor. With the right guidance, you’ll be well on your way to mastering this difficult section of math.

FAQs

If you still have questions about percentages, refer to our FAQ section below.

1. How Do You Determine a Percentage?

You can determine a percentage by taking the part you want the percentage of and dividing it by the total. Then convert the decimal to a percent.

For example, to find the percentage if you scored 32 out of 40 points on an exam:

32/40 = 0.80 ➡ 80%. You got 32 out of 40 questions right, which is 80%!

2. What Is Meant By Percentage?

A percentage represents a part out of 100. It expresses how much a part contributes to the total whole.

For example:

• 25% means 25 out of 100
• 50% means 50 out of 100

Percentages allow you to calculate proportions for scores, financial transactions like sales tax and tips, population statistics, and more.

3. Why Is It Important to Calculate Percentages?

Calculating percentages has many real-world applications, like analyzing exam scores, making financial decisions, tracking investments, interpreting statistics, and more.

Practicing how to take percentages of numbers and convert them between percentages, decimals, and fractions builds critical life math skills. Understanding percentages helps you quantify parts versus wholes.

Final Thoughts

Percentage problems are ubiquitous in everyday life situations that students will encounter. From calculating discounts and tips to understanding exam scores and savings goals, the ability to solve percent problems is an essential skill.

The key to mastering this skill is to break down complex problems into manageable steps and develop a systematic approach. Practice translating word problems into mathematical expressions, and always verify your solutions to ensure accuracy.

Proficiency in solving percentage problems not only prepares students for college admissions tests but also equips them with a valuable tool for future academic and professional endeavors. Investing time and effort into honing this foundational math skill will pay dividends in the long run, opening doors to success in higher education and beyond.