Brianna needs to earn a C in her Geology class. Her current test scores are 65, 67 67, and 93. Her final exam is worth 6 test scores. In order to earn a C Brianna's average must lie between 70 and 79 inclusive. What range of scores can Brianna receive on the final exam to earn a C in the course?
(65+67+67+93+6x)/10 = 70
(65+67+67+93+6x)/10 = 79
Solve for x in each case.
To find the range of scores Brianna can receive on the final exam to earn a C in the course, we need to calculate her overall average and determine the range of scores that would bring her average between 70 and 79.
First, let's calculate Brianna's current average test score by finding the average of her four test scores. Adding her four test scores together, we get:
65 + 67 + 67 + 93 = 292
To find the average, divide the total by the number of tests:
292 / 4 = 73
Brianna's current average is 73.
Now, we need to consider the impact of the final exam on her overall average. Since the final exam is worth 6 test scores and her average is currently based on 4 test scores, we need to add 6 times the average of the additional test scores to the current average.
Let's denote the range of scores Brianna can receive on the final exam as X. To find the range of scores, we can set up an inequality as follows:
(73 + 6X) / 10 ≥ 70 and (73 + 6X) / 10 ≤ 79
First, let's solve the first inequality:
(73 + 6X) / 10 ≥ 70
We can multiply both sides of the inequality by 10 to eliminate the fraction:
73 + 6X ≥ 700
Subtract 73 from both sides:
6X ≥ 700 - 73
6X ≥ 627
Now, let's solve the second inequality:
(73 + 6X) / 10 ≤ 79
Again, we can multiply both sides of the inequality by 10:
73 + 6X ≤ 790
Subtract 73 from both sides:
6X ≤ 790 - 73
6X ≤ 717
Now, divide both sides of both inequalities by 6:
X ≥ 627 / 6
X ≥ 104.5
X ≤ 717 / 6
X ≤ 119.5
So, the range of scores Brianna can receive on the final exam to earn a C in the course is between 104.5 and 119.5 (inclusive), or in interval notation: [104.5, 119.5].