Do you ever feel like algebra is just a bunch of meaningless equations and symbols? Well, think again! Algebra is actually all around us in everyday life. In this blog post, we will discuss seven examples of how algebra is used in the real world.
We will also provide real-life applications for each example. So whether you’re a student trying to understand why you’re learning this stuff or a teacher looking for ways to make it more relevant to your students, read on!
Examples of Algebra in everyday life
Whilst algebra has many applications in daily life, here are my favorite ways of using algebra to solve problems.
1. Calculating discounts at the store
You’re at the store and you see a shirt that’s on sale for 20% off. How much will it cost? This is a great opportunity to use some algebra!
Here’s how we can set this up:
Let x represent the original price of the shirt
Then, we know that:
x – 0.20x = the new price of the shirt
We can simplify x – 0.20x to 0.8x.
So then the new price of the shirt is 0.8x
If the original price of the shirt is $30,
then the new price of the shirt = 0.8 x 30 = $24
2. Are we there yet? Calculating how long it will take to get somewhere
Remember Bart Simpson asking ‘Are we there yet?’ on repeat.
Well, we can use algebra, specifically the formula linking distance, speed and time, to calculate how long it will take to arrive at your destination.
Say your car is traveling at 60 miles per hour, then the formula would be:
So instead of asking ‘Are we there yet?’, you could look out the window for a sign that shows how many miles to your destination then use the Distance-Speed-Time formula.
So the time to get to Las Vegas will be 72 divided by 60 which is just over 1. So it will be just over 1 hour to get there.
The distance – speed – time formula is a useful math formula to remember.
3. Figuring out how many pizzas to order
You’re having 7 friends over and you want pizza.
You each can eat at least 4 slices.
If there are 8 slices in a pizza, how many pizzas should you order?
You can use algebra to find how many pizzas you should order by writing an equation and solving it.
Let x represent the number of pizzas you should order.
So then you and 7 friends is 1 + 7, which is 8.
If each person eats 4 slices, the total number of slices is 8 x 4 = 32
Since each pizza has 8 slices, the number of slices in total will be 8x.
Here’s what it looks like as an algebraic equation:
So you will need to order at least 4 pizzas.
If your friend eat more than 4 slices each you need to order more pizzas.
If your mom and dad, brothers & sisters want pizza too, you will need to order more.
So we could write it as an algebraic inequality like this:
4. Calculating how many hours you need to work
Imagine there is a new pair of jeans you want that cost $75.
If your parents give you $25 towards them, how many hours of babysitting do you have to work in order to buy them?
Well you only need $50 right because $75 – $25 = $50
Let us say you earn $5 an hour for babysitting.
Then you will need to work for 10 hours.
Here’s what it looks like in algebra:
5. When adjusting amounts in a recipe when cooking
Let’s say you want to make some choc-chip cookies but the recipe requires 2 eggs and you only have 1 egg.
You will need to adjust the amounts of the rest of the ingredients.
This is a simple example where you can simply halve each ingredient.
Alternatively, you could use your knowledge of algebra to write an algebraic equation to calculate all the other quantities.
This is useful when its not a simple case of doubling or halving amounts.
For example if you wanted to make choc-chip cookies but you only have 2 cups of flour and you need 3 cups.
This means your recipe will be 2/3 of the original recipe.
So your formula will be:
new amount = 2/3 x recipe amount
6. Planning a budget and sticking to it
Budgeting is so important, whether you’re an individual, a family or a business. And algebra can help!
Let’s say you have $200 income in a month. You want to budget this out so that you don’t overspend and can even save money each month. Perhaps for an end-of-school holiday, a car or college.
Here’s how we can set this up:
List all your expenses, for example:
- $16 cell phone
- $30 monthly bus pass
- $50 going out with friends
Add up your expenses to find your monthly expenses.
16 + 30 +50 = 96
You should track your expenses in an app or spreadsheet to see what you are actually spending your money on. These days with apple pay and a cashless society it is very easy to spend money and not realize how much we are spending over. a month.
Subtract your total monthly expenses from your income to calculate the amount leftover that you can save (or invest).
Using algebra this could be done like this:
Let x represent your monthly expenditure.
Then we know that:
200-x = the amount we can save each month
Of course, this is just a simple example. In reality, you may use a spreadsheet (which is what I use). But you will need to understand the mathematics so you can enter a formula in your spreadsheet. This way when your expenses vary each month your savings will be automatically calculated.
So algebra can help you to create a budget, stick to it and even save or invest.
7. Comparing cell phone plans
The time will come when your parents stop paying your cell bill. In order to find the best value for money, you need to be able to compare different cell phone plans.
Algebra can help you do this!
Let’s say you’re looking at two different cell phone plans:
Plan A: $60/month with unlimited talk and text and 5GB data
Plan B: $20/month with unlimited talk and text and 1GB data plus $10/GB over this amount.
In order to compare cell phone plans, we need to find out how much data we use each month. You may need to look at past statements for this information.
Just say you use roughly 3GB of data each month.
On Plan A, the 3GB is included so your total bill would be $60
On Plan B, 3GB is over the 1GB of included data so you will need to pay extra. Each plan will have different costs.
The amount you will pay is calculated as follows:
# of GB over plan = 3GB minus 1GB = 2 GB
Cost for extra GB = 2 x $10/GB = $20
Total monthly cost = $20 + $20 = $40
So plan B ends up being $20 cheaper.
You could write this as a formula as:
Total monthly cost = 20 + (# GB used – 1GB) x 10
Since the amount of data used each month may vary, it Is called a variable.
Different plans may charge different excess data costs too.
You could set up a spreadsheet to calculate the different monthly costs for the varying amount of data used to help you decide which cell phone plan is best for your needs.
You can see that once you use over 5GB of data the monthly cost for plan B will be more than $60. This is when plan A is the best value.
So knowing how to write a formula can help you compare cell phone plans.
Wrapping up and my experience with using examples of Algebra in everyday life in the classroom.
There are countless other examples of how algebra is used in daily life. These are just a few of the ways that I use it on a regular basis to problem solve. I’m sure you can think of many more!
From my 14+ years of teaching high school mathematics to students of all abilities, I have observed that some students need to see the relevance of abstract concepts like Algebra in order to be interested.
Start the lesson with a hook or example of how they can use algebra in real life so they buy into the topic and are more engaged.
If you’re a teacher, try incorporating some real-life examples into your lessons. And if you’re a student, pay attention to the ways that you use algebra in your daily life. It will help you to better understand the concepts and make them more relevant to your own life.
I hope this article has helped you to see how algebra is used in everyday life.