In your class, you have scores of 72, 67, 85, and 76 on the first four of five tests. To get a grade of C, the average of the first five tests scores must be greater than or equal to 70 and less than 80.
- Solve an inequality to find the least score you can get on the last test and still earn a C
- What score do you need if the fifth test counts as two tests?
70 < (72 + 67+ 85 + 76 + x)/5 ≤ 80
70 < (300 + x)/5 ≤ 80
350 ≤ 300+x ≤ 400
finish it up
To find the least score you can get on the last test and still earn a grade of C, we need to ensure that the average of all five test scores is greater than or equal to 70 and less than 80.
1. Let's represent the fifth test score as "x". The average of the five tests can be calculated by adding up all the scores and dividing by 5:
(72 + 67 + 85 + 76 + x) / 5 ≥ 70
2. To solve this inequality, we can simplify it by multiplying both sides by 5 to get rid of the denominator:
72 + 67 + 85 + 76 + x ≥ 350
3. Combine like terms:
300 + x ≥ 350
4. Subtract 300 from both sides to isolate "x":
x ≥ 50
Therefore, the least score you can get on the last test and still earn a grade of C is 50 or above.
Now, let's consider if the fifth test counts as two tests:
1. We still need the average of all the test scores to be greater than or equal to 70 and less than 80.
2. Since the fifth test counts as two tests, we need to adjust the equation by adding the score twice:
(72 + 67 + 85 + 76 + 2x) / 7 ≥ 70
3. Simplify the inequality by multiplying both sides by 7:
72 + 67 + 85 + 76 + 2x ≥ 490
4. Combine like terms:
300 + 2x ≥ 490
5. Subtract 300 from both sides:
2x ≥ 190
6. Divide both sides by 2 to isolate "x":
x ≥ 95
Therefore, if the fifth test counts as two tests, you would need a score of 95 or above to earn a grade of C.