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 this course. Select the correct answer from the following
a) 80 less than or equal to 85 + 85 + 85 + 85 + x/5 less than or equal to 90; 85 less than or equal to x less than or equal to 110
b) 80 < 85 + 85 + 85 + 85 + x/5 < 90; 85 < x < 110
c) 90 less than or equal to 85 + 85 + 85 + 85 + x/5 less than or equal to 80; 110 less than or equal to x less than or equal to 80
d( 90 < 85 + 85 + 85 + 85 + x/5 < 80; 110 < x < 85
Show your work
Let x be the score she needs to make on the EOC.
To find her final average, we can set up the equation: (4/5)(85) + (1/5)(x) = average
Multiplying through by 5 to clear the fraction, we get: 4(85) + x = 5(average)
Simplifying, we have: 340 + x = 5(average)
Since the average needs to be between 80 and 90 inclusive, we have the compound inequality: 80 ≤ (340 + x)/5 ≤ 90
Multiplying through by 5, we get: 400 ≤ 340 + x ≤ 450
Next, we subtract 340 from all parts of the inequality: 400 - 340 ≤ x ≤ 450 - 340
Simplifying, we have: 60 ≤ x ≤ 110
Therefore, the correct answer is: b) 80 < 85 + 85 + 85 + 85 + x/5 < 90; 85 < x < 110
To find the possible score she will need to make on the EOC, we can set up a compound inequality.
Let's say the student's score on the EOC is represented by x.
The EOC counts for 1/5 of her overall grade.
Her class average counts for 4/5 of her overall grade.
We want her average to be between 80 and 90 (inclusive) after her EOC is entered.
So, the compound inequality can be written as:
80 ≤ (4/5) * 85 + (1/5) * x ≤ 90
Simplifying the inequality:
80 ≤ (340/5) + (x/5) ≤ 90
80 ≤ 68 + (x/5) ≤ 90
80 - 68 ≤ (x/5) ≤ 90 - 68
12 ≤ (x/5) ≤ 22
To find the possible score 'x', we can multiply both sides by 5, giving us:
12 * 5 ≤ x ≤ 22 * 5
60 ≤ x ≤ 110
Hence, the correct answer is:
a) 80 ≤ 85 + 85 + 85 + 85 + (x/5) ≤ 90; 60 ≤ x ≤ 110
To solve this problem, we need to set up a compound inequality that represents the range of scores the student can make on the EOC to achieve her desired average. Let's break down the problem step by step:
Step 1: Define the given information:
- The student scored 85 in her algebra class before the EOC.
- The EOC counts as 1/5 of her overall grade.
- The class average counts as 4/5 of her grade.
Step 2: Determine the range for her overall grade:
Based on the given information, we know that the class average counts 4/5 of her overall grade. So, her class average is (4/5) * 85 = 68.
Step 3: Set up the compound inequality:
We want the student's average to be between 80 and 90, inclusive. Therefore, the compound inequality can be written as:
80 ≤ (68 + x/5) ≤ 90,
where x represents the student's score on the EOC.
Step 4: Solve the compound inequality:
To solve the compound inequality, we'll isolate x by performing the necessary operations:
80 ≤ (68 + x/5) ≤ 90
-68 ≤ x/5 ≤ 22
Multiply all the terms by 5 to eliminate the fraction:
-68 * 5 ≤ x ≤ 22 * 5
-340 ≤ x ≤ 110
Step 5: Finalize the answer:
From the final compound inequality, we can see that the possible scores she will need to make on the EOC to get the desired average range from -340 to 110.
Therefore, the correct answer is:
a) 80 ≤ 85 + 85 + 85 + 85 + x/5 ≤ 90; 85 ≤ x ≤ 110
Are you sure the answer is not A instead of B.
I apologize for the confusion. You are correct, the correct answer is A instead of B.
The correct compound inequality is:
80 ≤ (85 + 85 + 85 + 85 + x/5) ≤ 90; 85 ≤ x ≤ 110
Thank you for pointing out the error.