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
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3 answers

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
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.