A student scored 85 in her Algebra class before she took the End of Course Exam (the EOC). The student wants her average to be between 80 and 90 inclusive after her EOC is entered into her grades. The EOC counts 1/5 of her overall grade and her class average counts 4/5 of her grade. Write and solve a compound inequality to find the possible score she will need to make on the EOC to get the average she wants for her final grade in the course.(1 point)
Responses
80 ≤85 + 85 +85 +85 + x5 ≤ 90
; 85 ≤ x ≤ 110
80 ≤85 + 85 +85 +85 + x5 ≤ 90
; 85 ≤ x ≤ 110
80 <85 + 85 +85 +85 + x5 < 90
; 85 < x < 110
80 <85 + 85 +85 +85 + x5 < 90
; 85 < x < 110
90 ≤85 + 85 +85 +85 + x5 ≤ 80
; 110 ≤ x ≤ 80
90 ≤85 + 85 +85 +85 + x5 ≤ 80
; 110 ≤ x ≤ 80
90 <85 + 85 +85 +85 + x5 < 80
; 110 < x < 85
The correct compound inequality is:
80 ≤ (85 + 85 + 85 + 85 + x)/5 ≤ 90
To solve this compound inequality, we can multiply all terms by 5 to eliminate the fraction:
400 ≤ 340 + x ≤ 450
Next, we can subtract 340 from all terms:
400 - 340 ≤ x ≤ 450 - 340
This simplifies to:
60 ≤ x ≤ 110
Therefore, the possible score she will need to make on the EOC to get the average she wants for her final grade in the course is between 60 and 110.
The correct compound inequality to find the possible score she will need to make on the EOC to get the average she wants for her final grade in the course is:
80 ≤ (85 + 85 + 85 + 85 + x)/5 ≤ 90
Explanation:
1. We know that the EOC counts for 1/5 of her overall grade and her class average counts for 4/5 of her grade. Therefore, we divide the sum of her class average and the EOC score by 5 to find the overall average.
2. The first inequality (80 ≤ (85 + 85 + 85 + 85 + x)/5) represents the minimum average she wants, which is 80.
3. The second inequality ((85 + 85 + 85 + 85 + x)/5 ≤ 90) represents the maximum average she wants, which is 90.
4. To solve the compound inequality, we multiply both sides of the inequalities by 5 to eliminate the fraction. This gives us:
400 ≤ 85 + 85 + 85 + 85 + x ≤ 450
5. We can simplify this to:
400 ≤ 340 + x ≤ 450
6. Next, we subtract 340 from all sides of the inequality:
400 - 340 ≤ 340 + x - 340 ≤ 450 - 340
60 ≤ x ≤ 110
7. Therefore, the possible score she will need to make on the EOC to get the average she wants for her final grade in the course is between 60 and 110 (inclusive), represented by the compound inequality 60 ≤ x ≤ 110.