In his algebra class, Rob has scores of 79, 85, 81, and 65 on his first four tests. To get a grade of C, the average of the first five tests must be greater than or equal to 70 and less than 80. Solve an inequality to find the range of scores that Rob can earn on the fifth test to get a C
Five tests with an average ≥70 means a total score of ≥ 5*70=350, but < 5*80 = 400.
He has already got:79 + 85 +81 + 65 = 310 points.
What should he get to score (x) between 350 and 400?
350 ≤ 310+x < 400
Subtract 310 from the above inequality to find the range of x.
942.5
Thank you very much for the step by step. Its make very easy to understand.
To find the range of scores that Rob can earn on the fifth test to get a grade of C, we need to solve an inequality based on the given conditions.
Let's assume Rob's score on the fifth test is represented by the variable "x".
To find the average of the first five tests, we need to add up all the scores and divide by the number of tests.
So, the inequality can be written as:
(79 + 85 + 81 + 65 + x) / 5 >= 70 and (79 + 85 + 81 + 65 + x) / 5 < 80
Let's simplify this inequality step by step:
Step 1: Adding up the scores:
(310 + x) / 5 >= 70 and (310 + x) / 5 < 80
Step 2: Multiplying both sides by 5 to eliminate the fraction:
310 + x >= 350 and 310 + x < 400
Step 3: Solving for x:
310 + x >= 350 => x >= 350 - 310 => x >= 40
310 + x < 400 => x < 400 - 310 => x < 90
Therefore, for Rob to get a grade of C, he must score between 40 (inclusive) and 90 (exclusive) on his fifth test.