Question

abby scored 87, 93, 96, and 89 on her first four history quizzes. what score does abby need to get on her fifth quiz to have an average of exactly 91 on her history quizzes
a. 90
b. 94
c. 98
d. 100

Explanation:

Step1: Recall average formula

The average $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $\bar{x}$ is the average, $x_{i}$ are the individual values and $n$ is the number of values. Here $n = 5$ and $\bar{x}=91$. Let the score on the fifth quiz be $x$. The sum of the first four - quiz scores is $87 + 93+96 + 89=365$.

Step2: Set up the equation

We know that $91=\frac{365 + x}{5}$.

Step3: Solve the equation

Multiply both sides of the equation by 5: $91\times5=365 + x$. So, $455=365 + x$. Then subtract 365 from both sides: $x=455 - 365=90$.

Answer:

A. 90