Applications of Algebra in Real Life (Uses & Examples)

One of the best ways to introduce your kids to the exciting world of math is to make it fun and relatable. Some kids don’t fall in love with math right away because they don’t understand the practical applications of math in real life. A student seeing algebra for the first time may even experience math anxiety. All those numbers and letters crammed together in mathematical equations can be intimidating; after all, it is like a foreign language. 

But imagine if we could give kids examples of algebra in real life to inspire them to have fun with numbers and letters—they may find they can do things they never dreamed possible, and of course, learn some amazing things along the way.

What is Algebra?

Before we get into some practical uses of algebra, let’s define it. Merriam-Webster defines algebra as:

“…a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.”

Simply put, algebra is still only arithmetic. However, the difference is that some numbers are represented by letters because their values are unknown or may be changed. These unknown values represented by letters are called variables. They allow one or more input values to be changed, altering the answer to the problem based on the inputs.

Each equation that you solve will have at least one target variable, which is the value for which you are trying to solve the problem. There may be other variables involved as well, which will be the variables that alter the value of the target variable as they are changed. Even for computers today, which run a lot of everything, basics of algebra is what powers them. While we humans are conditioned to naturally perform basic math such as – “2 teaspoons of sugar for 1 person implies 4 teaspoons, for 2 people”; machines need a more defined version of such “rules”.

These rules are nothing but simple algebraic statements.

Now that we have the definition out of the way let’s look at some practical uses for algebra in real life. 

[Read: Benefits of Math]

A Deliciously Simple Application of Algebra in Real Life

Imagine that you’re going to a big holiday feast, and you’re in charge of buying the groceries and cooking the meal. You have decided that the main course for the meal will be a nice juicy turkey. As you look around the supermarket to choose a turkey, you are disappointed to find only one remains. 

The weight on the package says that the turkey weighs 18 lbs. How can you determine how many people this turkey will feed so that nobody goes hungry at dinner? 

As a general rule of thumb, you need approximately 1.5 lbs of turkey for each person. You pull out a piece of paper and a pen and write down the following algebraic equation:

What you have just performed is one of the most basic, real-life uses for algebra. A variable value, x, represents the number of people who can be fed with an 18 pound turkey if we assume that 1.5 lbs are needed for each person. In this case, we have solved for x to determine that our 18 pound turkey can feed a total of 12 people.

While this example may seem trivial, it illustrates that we often use algebra without realizing it. Thanks to experience, we often do these quick computations in our heads, but at the root of what we are solving is an algebraic equation. Now, look ahead to the next part of our holiday dinner preparation for another application of algebra that you can use in real life.

An Algebraic Recipe for Tasty Results

You have finished your grocery trip and returned home from the supermarket to prepare the big feast. The turkey is stuffed and ready to go in the oven, and the potatoes are cooked, but you still have to make your famous homemade cranberry sauce. 

As you are about to begin following your recipe, you notice that it only makes enough cranberry sauce for four servings—but you will have a total of twelve people to feed. Before the anxiety kicks in you rely on math to save the day. 

You know that you need to make a larger batch, which means using more of each ingredient. Glancing over your recipe, you notice that it calls for 3 cups of cranberries to be used for four servings. So, how do you determine how much you need to use to feed all twelve people? 

Using a pen, you jot down the following on the back of the recipe card:

This time you decided to write an equation using two variables. The variable y represents the total number of cups of cranberries you should use in your recipe. It is the target variable in this equation. 

The variable x represents the number of diners that you are trying to feed. The beauty of this equation is that any time you need to cook your recipe for more than four people, you can always change the value of x to the number of people for whom you are cooking. This will allow you to determine how many cups of cranberries to use on that occasion.

Cool, huh?

[Read: Use of Calculus in Daily Life]

The Roadtrip Conundrum

You are planning a road trip to visit some relatives on the other side of the state. Due to the drive’s distance, you decide that it would be wise to put as much gasoline as possible into your vehicle before you leave town. You pull up to the gas pump and notice that the price is $3.10 per gallon of gas. You reach into your pocket and pull out a total of $30.45.

However, before you begin to fill your car’s gas tank, you decide that you should probably check your engine oil level too. When you pull the oil dipstick out, you can see that your oil is low by approximately a quart. Not wanting to run into issues while out on the road, you go into the gas station to purchase a quart of oil for your car. It costs $7.25.

You now have some concerns that you have spent too much on the oil and now may not have enough leftover to purchase enough gasoline to reach your destination. You decide to use algebra to determine how many gallons of gas you can put in your car.

The variable x represents the number of gallons of gas you can afford to put in your car. Because the cost of the gas is $3.10 per gallon, multiplying the per-gallon rate by a variable x value will give you the total cost. This calculation represents the number of gallons that can be purchased. 

You also needed to account for the quart of oil you purchased, so this was factored into the equation by adding it to your total gas cost to obtain the total sum of money spent at the gas station.

Because the idea was to get as much gas as possible, you began by setting the total cost to the total amount of money with which you began. This constant value ensures that you will be getting as much gasoline as you can afford. 

This problem was just another example of the many uses of algebra that you are likely to come across in life. There are many other scenarios that you encounter daily. However, the idea of algebra does not cross your mind because you are not accustomed to thinking in terms of variables. With a little thought and reasoning through each problem, you will find hints of algebra presenting itself almost daily.

[Read: Uses of Trigonometry]

Knowledge is Power

While you may not write down equations and variables each time you encounter one of these situations, algebra is mentally happening as you reason through these real-life events. It is therefore useful to understand how to solve for unknown values or variables even if the actual computations are done in your head. 

There are, however, times when you may write out and solve algebraic equations daily, depending on what career path you choose. Engineers use algebra to calculate trajectories and velocities of moving objects. Carpenters use algebra to determine quantities of materials needed, such as the number of floorboards needed to cover a room with given square footage. 

At BYJU’S FutureSchool, students are offered an extensive curriculum to help master the concepts of algebra and overcome math anxiety. This specially designed coursework will utilize challenges and leadership opportunities to give you the comfort and confidence to solve any algebra problem that comes your way.

The next time you do any math in your head, take a second to think about why you know how to solve that particular problem. Chances are, if you think through the reasoning behind the math, you will find that you could express it as an algebraic equation.