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)
Let x be the score the student needs to make on the EOC.
The student's overall grade will be 1/5*x + 4/5*85.
The inequality for the student's average grade is 80 <= (1/5*x + 4/5*85) <= 90.
Multiply equation by 5 to remove the fraction: 400 <= x + 4*85 <= 450.
Simplify the equation: 400 <= x + 340 <= 450.
Subtract 340 from all sides: 60 <= x <= 110.
The possible score the student needs to make on the EOC is between 60 and 110 inclusive. Answer: \boxed{60 \le x \le 110}.
To find the possible score the student needs to make on the EOC, we can set up a compound inequality.
Let's assume the score on the EOC is represented by the variable "x".
According to the problem statement, the EOC counts as 1/5 of her overall grade, and her class average counts as 4/5 of her grade.
To find the overall grade after the EOC is entered, we can use the following equation:
(4/5) * (Class average) + (1/5) * (EOC score) = Final average
Substituting the given values, we have:
(4/5) * 85 + (1/5) * x = Final average
Now, since the student wants her average to be between 80 and 90 inclusive, we set up the following compound inequality:
80 ≤ (4/5) * 85 + (1/5) * x ≤ 90
To solve this inequality, we need to isolate the variable "x" in the middle.
Let's start by subtracting (4/5) * 85 from all parts of the inequality:
80 - (4/5) * 85 ≤ (4/5) * 85 - (4/5) * 85 + (1/5) * x ≤ 90 - (4/5) * 85
This simplifies to:
80 - 68 ≤ (1/5) * x ≤ 90 - 68
12 ≤ (1/5) * x ≤ 22
To get rid of the fraction, we can multiply all parts of the inequality by 5:
12 * 5 ≤ (1/5) * 5 * x ≤ 22 * 5
60 ≤ x ≤ 110
So, the possible scores the student can get on the EOC to have an average between 80 and 90 inclusive are from 60 to 110.
Let x be the score the student needs to make on the EOC.
The grade for the EOC is 1/5 of her overall grade, so its contribution to her average is (1/5)x.
Her class average is 4/5 of her overall grade, so its contribution to her average is (4/5)(85).
To find the average score the student wants, we add these two contributions:
[(4/5)(85)] + [(1/5)x].
The average score the student wants is between 80 and 90, inclusive, so the compound inequality is:
80 ≤ [(4/5)(85)] + [(1/5)x] ≤ 90.
Now we can solve for x:
80 ≤ [(4/5)(85)] + [(1/5)x] ≤ 90.
80 ≤ (340/5) + (1/5)x ≤ 90.
80 ≤ (68) + (1/5)x ≤ 90.
80 - 68 ≤ (1/5)x ≤ 90 - 68.
12 ≤ (1/5)x ≤ 22.
To isolate x, we multiply all sides of the inequality by 5 (since the coefficient of x is 1/5):
5(12) ≤ 5[(1/5)x] ≤ 5(22).
60 ≤ x ≤ 110.
Therefore, the student needs to score between 60 and 110 on the EOC to get an average between 80 and 90 inclusive for her final grade in the course.