Question

rex is currently taking physics as one of his electives in school. his grade at the end of the year is determined by the average of four exams, each worth 100 points. on his first test he got an 84, on his second he got a 86, and on his third an 92. what must he score on his fourth exam to get an a (90%) in the course?
a. 98
b. 90
c. 88
d. 86

please select the best answer from the choices provided

a
b
c
d

Explanation:

Step1: Recall the average formula

The average of four numbers \( x_1, x_2, x_3, x_4 \) is \( \frac{x_1 + x_2 + x_3 + x_4}{4} \). We know the desired average is 90, and the first three scores are 84, 86, and 92. Let the fourth score be \( x \). So we set up the equation: \( \frac{84 + 86 + 92 + x}{4}=90 \).

Step2: Multiply both sides by 4

Multiply both sides of the equation by 4 to eliminate the denominator: \( 84 + 86 + 92 + x = 90\times4 \). Calculate the right - hand side: \( 90\times4 = 360 \). Then calculate the sum of the left - hand side numbers: \( 84+86 = 170 \), \( 170 + 92=262 \). So the equation becomes \( 262+x = 360 \).

Step3: Solve for x

Subtract 262 from both sides of the equation: \( x=360 - 262 \). Calculate \( 360-262 = 98 \).

Answer:

A. 98