# A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test?

Jul 6, 2016

She must earn a score of $82$ on her fourth test.

#### Explanation:

To have an average of $87$,
if we call the 4th test results $f$
then
$\textcolor{w h i t e}{\text{XXX}} \frac{87 + 81 + 88 + f}{4} = 87$

$\textcolor{w h i t e}{\text{XXX}} 256 + f = 87 \times 4 = 348$

$\textcolor{w h i t e}{\text{XXX}} f = 82$