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 ≤ 11080 ≤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
80 ≤ 85 + 85 + 85 + 85 + (x/5) ≤ 90
80 ≤ 340 + (x/5) ≤ 90
80 - 340 ≤ (x/5) ≤ 90 - 340
-260 ≤ (x/5) ≤ -250
-260 * 5 ≤ x ≤ -250 * 5
-1300 ≤ x ≤ -1250
The correct compound inequality to find the possible score the student will need to make on the EOC is:
80 ≤ (85 + 85 + 85 + 85 + x)/5 ≤ 90
To solve this compound inequality, we can multiply all the terms by 5 to get rid of the fraction:
400 ≤ 85 + 85 + 85 + 85 + x ≤ 450
Next, we can simplify the expression by adding the numbers together:
400 ≤ 340 + x ≤ 450
Now, we can isolate the variable:
400 - 340 ≤ x ≤ 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.
To solve this problem, we can set up a compound inequality. Let's say the student's EOC score is represented by the variable x.
We are given that the EOC counts 1/5 of her overall grade and her class average counts 4/5 of her grade. So, the average is calculated as (4/5)(85) + (1/5)(x).
We want the average to be between 80 and 90 inclusive, so we can write the compound inequality as follows:
80 ≤ (4/5)(85) + (1/5)(x) ≤ 90
Now, let's solve this inequality step by step:
Step 1: Distribute the fractions.
80 ≤ (340/5) + (x/5) ≤ 90
Step 2: Simplify the expression.
80 ≤ 68 + (x/5) ≤ 90
Step 3: Subtract 68 from all parts of the inequality.
80 - 68 ≤ (x/5) ≤ 90 - 68
12 ≤ (x/5) ≤ 22
Step 4: Multiply all parts of the inequality by 5 to eliminate the fraction.
5(12) ≤ x ≤ 5(22)
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.