Question

Awilda has grades of 94 and 88 on her first two calculus tests what possible scores on a third test will give her an average of at least 90

Answer 1

If she wants to average 90 for three tests, then the three scores must add up to

(3 x 90) = 270 .

Of the 270 points that she needs, she already has (94 + 88) = 182 on the first 2 tests.

She needs (270 - 182) = 88 more on the third test to achieve an average of 90 for all three tests. Any score of 88 or higher on the third test will give her an average of at least 90 for all three.

The highest average she can possibly wind up with is 94 . If she scores a perfect 100 on the third test, then her total score on all three tests will be

(94 + 88 + 100) = 282

and her three-test average will be (282/3) = 94 .

Answer 2

To find the average of three scores, add the three scores and divide the sum by 3. Let the score of the third test be x.

$\dfrac{94 + 88 + x}{3} \ge 90$

$\dfrac{x + 182}{3} \ge 90$

$x + 182 \ge 270$

$x \ge 88$

Answer: The score must be at least 88.