Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Brad has scored 87, 89, and 78 on the first three. What range of scores on the fourth test will give Brad a C for the semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.

Answer 1

Answer:

$26\leq x\leq 62$

Step-by-step explanation:

Let x represent Brad's score on 4th test.

We have been given Brad has scored 87, 89, and 78 on the first three.

To find the range of Brad's test score, we will represent our given information in an inequality as:

$70\times 4\leq 87+89+78+x\leq 79\times 4$

$280\leq 254+x\leq 316$

$280-254\leq 254-254+x\leq 316-254$

$26\leq x\leq 62$

Therefore, the range of score on the fourth test will be $26\leq x\leq 62$.