## Using Algebra With Averages

April 28th, 2012

There are certain kinds of linear equations in Algebra that you can get as the result of trying to figure out something to do with an average. A classic example of this type of problem is the following: You receive five grades in a class for an average of 91. Four of the grades were 90, 85, 92 and 100. What was the fifth grade?

To solve this problem, you’ll need to set up an equation based on the fact that the sum of the five grades divided by five equals 91. Here’s what you should get.

$\frac{x + 90 + 85 + 92 + 100}{5} = 91$

Do the addition on the top and you’ll get:

$\frac{x + 367}{5} = 91$

Now you have a pretty standard linear equation to solve. Start by multiplying both sides by five.

$\frac{x + 367}{5} * 5= 91 * 5$ $x + 367 = 455$

And then subtract 367 from both sides.

$x + 367 - 367 = 455 - 367$ $x = 88$

Once you have this answer, you’ll need to check it by plugging it into the original equation to make sure that it works correctly.

Related posts: