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

Answer:

between 62 and 98.

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:

$B=\frac{94 + 77 + 87 + X}{4}$

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

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.