Question

1. to get an a in a course, you must have an average of at least 90 points for 4 tests of 100 points each. for the first 3 tests, your score are 87, 92, and 84. what must you score on the fourth test to earn a 90% average for the course?

Explanation:

Step1: Recall the average formula

The average of \( n \) numbers \( x_1, x_2, \dots, x_n \) is \( \frac{x_1 + x_2 + \dots + x_n}{n} \). Here, \( n = 4 \), and the average should be at least 90. Let the score on the fourth test be \( x \).

Step2: Set up the inequality

The sum of the first three scores is \( 87 + 92 + 84 \), and the sum of all four scores is \( 87 + 92 + 84 + x \). The average is \( \frac{87 + 92 + 84 + x}{4} \geq 90 \).

Step3: Solve the inequality

First, calculate the sum of the first three scores: \( 87+92 + 84=263 \). So the inequality becomes \( \frac{263 + x}{4}\geq90 \). Multiply both sides by 4: \( 263+x\geq360 \). Subtract 263 from both sides: \( x\geq360 - 263 \), so \( x\geq97 \).

Answer:

You must score at least 97 on the fourth test.