Question

The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average for this exam was 72. Set up an equation to solve for the highest and lowest scores. Show your original equation and the process used to find the highest and lowest exam score.

Answer 1

Answer:

The highest score is 91 and the lowest score is 53  

Step-by-step explanation:

The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average is 72.

1. The method used to solve this question, is the use of absolute values.

2. Let x be the value that we can use to represent the lowest and highest scores. The equation using absolute values is given as:

| x - 72 | = 19.

Therefore:

x - 72 = 19 (highest score) or

- (x - 72) = 19 (lowest score)

3. We have to find the value of x for which it is the highest or lowest score.

The highest score is given as:

x - 72 = 19

x = 19 + 72

x = 91

For lowest score:

-(x - 72) = 19

-x + 72 = 19

x = 72 - 19

x = 53

The highest score is 91 and the lowest score is 53