Question

on the first four point quizzes, Mat made a 75, 86, 99, and 89. Write and solve an equation to find the score Matt needs on the fifth quiz to have a mean of 93.

Answer 1

The formula for the mean of data is,

$Mean=\frac{Sumofnumbers}{Amount\text{ of numbers}}$

Therefore,

The sum of the five points is,

$75+86+99+89+x=349+x$

The amount of quiz is 5.

Given

$Mean=93$

Therefore,

$93=\frac{349+x}{5}$

Evaluate for x

$\begin{gathered} \mathrm{Multiply\:both\:sides\:by\:}5 \\ \frac{5\left(349+x\right)}{5}=93\times\:5 \\ \mathrm{Simplify} \\ 349+x=465 \\ \mathrm{Subtract\:}349\mathrm{\:from\:both\:sides} \\ 349+x-349=465-349 \\ \mathrm{Simplify} \\ x=116 \end{gathered}$

Hence, the fifth quiz is 116.