Question # Self-Check A student scores 82, 96, 91, and 92 on four college algebra exams. What score is needed on a fifth exam for the student to earn an average grade of 90?

Upper level algebra
ANSWERED Self-Check A student scores 82, 96, 91, and 92 on four college algebra exams. What score is needed on a fifth exam for the student to earn an average grade of 90? 2020-10-19

Approach:
Let's assume that a student needs to score x on the fifth exam.
We will use the following formula for calculating average.
$$\displaystyle{A}{v}{e}{r}{a}\ge={\frac{{{S}{u}{m}\ {o}{f}\ {s}{c}{\text{or}}{e}{s}}}{{{N}{u}{m}{b}{e}{r}\ {o}{f}\ {e}{x}{a}{m}{s}}}}$$
Calculation:
$$\displaystyle{A}{v}{e}{r}{a}\ge={\frac{{{S}{u}{m}\ {o}{f}\ {s}{c}{\text{or}}{e}{s}}}{{{N}{u}{m}{b}{e}{r}\ {o}{f}\ {e}{x}{a}{m}{s}}}}$$
$$\displaystyle{90}={\frac{{{82}+{96}+{91}+{92}+{x}}}{{{5}}}}$$
$$\displaystyle{90}={\frac{{{361}+{x}}}{{{5}}}}$$
$$\displaystyle{90}\times{5}={361}+{x}$$
$$\displaystyle{450}={361}+{x}$$
$$\displaystyle{x}={450}-{361}$$
$$\displaystyle{x}={89}$$
Final Statement:
A student needs to score 89 on the fifth college exam.