02 Relation between two quantities

Relating two quantities to make an equation

Equations help us understand how two things are related to each other. For instance, the amount of money you pay for electricity depends on how much electricity you use. Sometimes, the relationship between two things isn’t so simple, but we can still use equations to figure it out.

Let’s look at an example. If one pen costs 2 dollars, then two pens will cost 4 dollars, three pens will cost 6 dollars, and so on.

No matter how many pens you buy, the price will always be double that amount (unless a discount is offered). You can figure out how many pens you can buy for a certain price, or how much a certain number of pens will cost you. Keep in mind that in both cases, one of the quantities has to be known. To make it simpler for all cases, we can use a letter (placeholders) to stand in for the number of pens and the price and form an equation. price of pens = 2 x (number of pens) If we use 𝑥 to represent the number of pens and y to represent the price, the equation would look like this: y = 2𝑥.

Let’s talk about another example! If we have 240 candies and we want to share them with a group of ‘t’ students, we can use an equation to figure out how many candies each student gets.

But here’s the thing: unlike before, where increasing the number of pens increased the price as well, in this case, the more students there are, the less candy each student gets. It’s just common sense, right? For example, if there are only two students, they each get 120 candies. But if there are 20 students, they only get 12 candies each. See how the number of candies each student gets goes down as the number of students goes up?

It’s like a pattern! No matter how many students there are, the product of the number of students and the number of candies each student gets has to equal 240. This is maintained because the number of times by which the number of students increases, the candies received by each student decrease by the same factor.

So, we have number of candies each student receives x number of students = total number of candies If we replace the number of candies each student receives with a placeholder p, we get the equation p x t = 240. Now we can replace the value of either of the two quantities and find the value of the other.