What can I do with Algebra?

Is math really all around you? Well, let’s take a moment to think about it. Pretend you don’t know what math is and I tell you math is descriptive language. What is a descriptive language you ask? Well, it is language used in such a way that it can help someone feel like they are part of the scene being described. If done right, it can evoke emotions and create a reality beyond the language itself. To do all this fantastic magic, descriptive language uses descriptive words like adjectives, adverbs or descriptive verbs to enrich the story.

So, the take away here is that math is a language that can be used to create a reality and even evoke emotions. This is why some people cry when they take math tests. Yes, it is a bad joke, but a joke all the same, so two points for Gryffindor! Bad jokes aside, how does this relate to anything useful? Suppose you need to get the bus at 8 AM every day and you get up at 6:30 AM. In these 90 minutes, you have to shower/brush teeth, get ready, make & have breakfast, pack lunch, walk the dog and catch the bus. A few things are typically out of your control such as the bus arriving on time and the dog cooperating, which can eat into your 90 minutes.

You can create a simple equation to describe this problem – and yes, it is a problem if you miss the bus. 90 to 95 minutes = (20 minutes: shower/brush teeth) + (20 minutes: get ready) + (20 minutes: make & have breakfast) + (10 minutes: pack lunch) + (10 to 15 minutes: walk dog) + (10 minutes: walk to the bus).

The equation above gives a good idea of how much time can be taken in total, but how do you describe this in math? You use Algebra! Assume that the time the dog takes is t minutes and the total time spent doing all the morning’s tasks is T, then we have the following:

 T = 20 + 20 + 20 + 10 + t + 10, and 90 ≤ T ≤ 95

→ T = 80 + t; 90 ≤ T ≤ 95

→ 90 ≤ 80 + t ≤ 95

→ 10 ≤ t ≤ 15

So, the time the dog takes is between 10 to 15 minutes. Why is this skill valuable? Well, what if you had to plan a more complex operation that had more variables like t1 = time to walk the dog and t2 = time to walk to the bus stop? Then you have:

 T = 20 + 20 + 20 + 10 + t1 + t2, and 90 ≤ T ≤ 95

→ T = 70 + t1 + t2; 90 ≤ T ≤ 95

→ 90 ≤ 70 + t1 + t2 ≤ 95

→ 90 - 70 ≤ t1 + t2 ≤ 95 - 70

→ 20 ≤ t1 + t2 ≤ 25

Now you know that between the dog and the walk to the bus you have 25 minutes to play with. So, if the dog takes long, you know you have to book it to the bus stop, or if the dog is quick, you can stroll to the bus stop. But do you really have 25 minutes? Not unless you wake up earlier. You only have 90 minutes, so you need to modify your equation to take that into account.

T = 20 + 20 + 20 + 10 + t1 + t2, and T ≤ 90

→ T = 70 + t1 + t2; T ≤ 90

→ 70 + t1 + t2 ≤ 90

→ t1 + t2 ≤ 90 - 70

→ t1 + t2 ≤ 20

You really have only 20 minutes between the dog and the bus. The reason I did the circuitous steps is to introduce the concept of inequalities and the need to fully understand the word problem while keeping an eye on the given values. Tricksy Hobbits indeed.