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)

Question

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)

Answer 1

Let x be the score the student needs to make on the EOC.

Her overall grade will be calculated as (4/5)*(85) + (1/5)*(x).
The inequality to find the possible score she will need to make on the EOC is:
80 ≤ (4/5)*(85) + (1/5)*(x) ≤ 90
Simplifying the inequality:
68 + (1/5)*(x) ≤ 90
Subtracting 68 from all parts of the inequality:
1/5*x ≤ 22
Multiplying both sides of the inequality by 5:
x ≤ 110
So the possible score the student will need to make on the EOC to get the average she wants for her final grade in the course is x ≤ 110.

Answer 2

To solve this problem, we can set up a compound inequality to represent the possible scores she will need to make on the EOC.

Let's call the score she needs to make on the EOC "x".

Given that the EOC counts 1/5 of her overall grade and her class average counts 4/5 of her grade, we can calculate her final grade using the following equation:

(4/5) * 85 + (1/5) * x = average

Now, we know that her average needs to be between 80 and 90 inclusive. So, we can set up the following compound inequality:

80 ≤ (4/5) * 85 + (1/5) * x ≤ 90

To solve this compound inequality, we can begin by simplifying the equation:

80 ≤ (4/5) * 85 + (1/5) * x ≤ 90
80 ≤ 340/5 + (1/5) * x ≤ 90
80 ≤ 68 + (1/5) * x ≤ 90

Now, let's isolate the variable (1/5) * x:

80 - 68 ≤ (1/5) * x ≤ 90 - 68
12 ≤ (1/5) * x ≤ 22

To remove the fraction, we can multiply every term by 5:

5 * 12 ≤ 5 * (1/5) * x ≤ 5 * 22
60 ≤ x ≤ 110

Therefore, the possible score she will need to make on the EOC to get the average she wants is between 60 and 110 inclusive.

Answer 3

Let's denote the score the student needs to make on the EOC as x.

According to the given information, the EOC counts for 1/5 of the overall grade, and the class average counts for 4/5 of the overall grade.

To find the student's final grade, we can use the following equation:

(4/5)*85 + (1/5)*x

We want the final grade to be between 80 and 90 inclusive. Therefore, we can set up the compound inequality:

80 <= (4/5)*85 + (1/5)*x <= 90

Now, let's solve the compound inequality.

First, let's simplify the expression:

(4/5)*85 + (1/5)*x = (4/5)*85 + (x/5)
= (340/5) + (x/5)
= (340 + x)/5

Now, let's rewrite the compound inequality using the simplified expression:

80 <= (340 + x)/5 <= 90

To remove the fraction, let's multiply all the terms in the inequality by 5:

5*80 <= (340 + x)/5 * 5 <= 5*90
400 <= 340 + x <= 450

Next, let's simplify the inequality:

400 - 340 <= 340 + x - 340 <= 450 - 340
60 <= x <= 110

Therefore, the possible score the student 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.