Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Alice has scored 94, 77, and 87 on the first three. What range of scores on the fourth test will give Alice a B for the semester (an average between 80 and 89, inclusive)? Assume that all test scores have a non-negative value.

Answer 1

Alice needs to score between 62 and 98 on her fourth test to obtain a B grade for the semester, as all test scores are equally weighted in determining her final grade.

Step-by-step explanation:

To determine the range of scores Alice needs on her fourth test to achieve a B grade for the semester, we first calculate the total points she has so far. Alice has scored 94, 77, and 87 on the first three tests.

The sum of these scores is 94 + 77 + 87 = 258. Since the class is based on equally weighted tests, we can find the range of scores for the fourth test by calculating the necessary total points to reach an average of 80 and 89 respectively, for a B grade.

To have at least an 80 average, Alice needs 4 * 80 = 320 points in total. Thus the minimum she needs on the fourth test is 320 - 258 = 62 points.

For a maximum average of 89, Alice needs 4 * 89 = 356 points in total . Therefore, the highest score she can get and still receive a B is 356 - 258 = 98 points.

As a result, Alice needs to score between 62 and 98 on her fourth test to secure a B grade.

Answer 2

between 62 and 98.

Step-by-step explanation:

This question can be solved faily easy:

We denote "B" as the value average of the four test values for B score (between 80 - 89) and "X" as the score on the 4th test so to find the range of values that Alice needs to score in the 4th test we only have to replace in the next formula:

`B=(94 + 77 + 87 + X)/(4)`

`X=4*B-94-77-87`

We reformulate the equation in function of B

We have the next range of values for "B" (80, 81, 82, 83, 84, 85, 86, 87, 88, 89), we replace those values in the formula and operate to get the range of values we need to score in the 4th test.

`X=4*80-94-77-87=62`

`X=4*81-94-77-87=66`

`X=4*82-94-77-87=70`

`X=4*83-94-77-87=74`

`X=4*84-94-77-87=78`

`X=4*85-94-77-87=82`

`X=4*86-94-77-87=86`

`X=4*87-94-77-87=90`

`X=4*88-94-77-87=94`

`X=4*89-94-77-87=98`

As we can see for Alice to get a B for the semester she needs to score on the 4th test a score between 62 and 98 points.