Independent and Dependent Variables Examples

Tara throws a party every month. She's a little desperate for attention. The number of cupcakes she bakes for her guests depends on how many kids will be at the party. Tara likes to have two cupcakes per kid. She would also like to have some adult friends, but good luck with that, Tara. How should we express this situation algebraically?

In situations where one quantity depends on another, we can express this dependence in symbols, using a variable for each quantity. What we find ourselves with is an equation.

Let's call c the total number of cupcakes and k the total number of kids.

Our equation would be c = 2k, because Tara wants two cupcakes per kid.

Since the number of kids at the party can vary from month to month, k varies. Since c depends on k, c varies also. Here's hoping Tara gets a lot of k next month and needs to make a boatload of c's. Go get 'em, Tara.

Notice that we used letters for our variables that were chosen specifically to remind us what they represented: c for cupcakes and k for kids. We've mainly been using x and y all along, but there's no rule saying we can't give the rest of the alphabet a chance. So, whenever possible, use variables that seem more intuitive. Your brain will thank you for it.

Fred and John are brothers. John, who is the older of the two and was largely deprived of attention as a young boy, is constantly trying to one-up Fred. Both brothers enjoy clothes shopping. However, because of John's competitiveness, every time Fred buys a new pair of jeans, John will go out and buy a pair that's exactly $10 more expensive.

Express in symbols the relationship between the amount of money Fred spends on a pair of jeans and the amount of money John spends on a pair of jeans. Let F be the amount of money Fred spends, and J the amount of money John spends.

J = F + 10.