Algebra Problem Solving: Guess & Check

Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Stuck on a multiple choice question? Sometimes using the guess and check method is the fastest and easiest way to solve it. In this lesson, we'll practice using this method with a variety of algebra problems.

What is Guess and Check?

It can be frustrating to face a multiple choice math problem that you don't know how to solve. Somewhere, right in front of you in the answer choices, is the correct answer. But which one is it? It's just like Goldilocks looking at three bowls of porridge. She knew the right porridge was there, but which one was it?

Fortunately, there aren't three angry bears lurking outside your math test. Even better, you don't always need to know the exact way to solve a problem. Instead, you can use a shortcut method called guess and check.

Also known as back solving, guess and check works just like it sounds. It's basically what Goldilocks did. You take an answer choice and plug it in to the question, like tasting porridge to see if it's right. Just keep trying answers until you find the one that works. It can be a bit different with different types of problems, so let's look at a few.

Example #1

One of the times guess and check is especially useful is with quadratic equations. For example, this problem:

Which of the following is a possible solution for the equation x2 - 28 = -3x?

The answer choices are 7, 4, 2, 0 and -1.

Why is guess and check good here? The answer choices are just numbers. If the problem had variables or other more complex answer choices, this method wouldn't help. To solve this without guess and check, you'd need to set the equation equal to zero, then factor, then solve.

Let's just try plugging in numbers. Let's start with the middle number, 2:

22 - 28 = -3(2).

4 - 28 = -6

-24 = -6

It looks like 2 is too small, so let's try going larger and use 4:

42 - 28 = -3(4)

16 - 28 = -12

-12 = -12

That's it! 4 is the correct answer.

Example #2

Here's a question: In a hot wing eating contest, Natasha ate 9 more wings than Josh and twice as many as Lucas. Combined, they ate 46 wings. How many did Natasha eat?

The answer choices are: 10, 12, 16, 22 and 28.

To solve this, you need to set up an equation. This is a situation when it might be faster and easier to guess and check. Rather than start with 10, let's start in the middle with 16. Why? Watch what happens. If Natasha ate 16, then Josh ate 9 fewer, or 7. Lucas ate half of 16, or 8. 16 + 9 + 7 isn't close to 46. So 16 is too small. By that logic, 10 and 12 will also be too small.

As with Goldilocks, some answers might be too small, some too big. The faster we can narrow our choices to the 'just right' number, the better. If Goldilocks started with the porridge in the middle, she would've learned much faster.

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