Question

average example
in a physics course, a student scored 90 on one test, 88 on another test, and 82 on each of the other tests. the student’s test average for the course, where each test is weighted equally, is exactly 84. what is the total number of tests that the student has taken in the course?
f 5
g 6
h 7
j 9
identify average
setup
\\(\frac{90 + 88 + 82}{x}=84\\)

Explanation:

Step1: Set up the average - formula equation

Let the number of tests be $x$. The sum of the scores is $90 + 88+82(x - 2)$ (since there are two non - 82 scores and $x-2$ scores of 82), and the average is 84. So the equation is $\frac{90 + 88+82(x - 2)}{x}=84$.

Step2: Expand the numerator

$90 + 88+82x-164 = 84x$. Simplify the left - hand side: $(90 + 88-164)+82x=84x$, which gives $14 + 82x=84x$.

Step3: Solve for $x$

Subtract $82x$ from both sides: $14=84x - 82x$, so $2x = 14$, and $x = 7$.

Answer:

H. 7