Question

Noel Womack scored 87,96,86,92, and 93 in English 101. What must he score on the last test to earn an average score of 92?

Answer 1

The arithmetic average of a set of n numbers is \[\frac{a_1+a_2+...+a_n}{n}\]You have the situation where you want an average of 92, and you know, in the end, you'll have six scores (so n will be 6), and you have the first five terms. All you need to do is substitute in and solve:\[92=\frac{87+96+86+92+93+x}{6} =\frac{454+x}{6}\]Solve for x:\[92 \times 6 -454 =x \rightarrow x=98\]