a student scored 85 in her algebra class before she took her end of course exam. the student wants her average to be between 80 and 90 inclusive after the exam is entered into her grades. the exam counts as 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 exam to get the desired average in the course
Let x be the score she needs to make on the exam.
The average is calculated as:
(4/5 * 85) + (1/5 * x) = average
(4/5 * 85) + (1/5 * x) = 80
(4/5 * 85) + (1/5 * x) = 90
Multiply both sides of the first equation by 5 to eliminate the fraction:
(4/5 * 85) * 5 + (1/5 * x) * 5 = 80 * 5
Multiply both sides of the second equation by 5 to eliminate the fraction:
(4/5 * 85) * 5 + (1/5 * x) * 5 = 90 * 5
Multiply both sides of the equation by 5 to eliminate the fractions:
4 * 85 + x = 400
4 * 85 + x = 450
Simplify the equations:
340 + x = 400
340 + x = 450
Subtract 340 from both sides:
x = 60
x = 110
Thus, the possible score she needs to make on the exam to get the desired average in the course is between 60 and 110.
Let's solve the problem step by step.
Let's denote the student's score on the end of course exam as "x". The student's average grade in the class is represented by the equation:
(4/5) * (average grade in class) + (1/5) * (exam score) = final average
We know that the average grade in the class before taking the exam is 85, so we can substitute the values into the equation:
(4/5) * 85 + (1/5) * x = final average
The student wants her average to be between 80 and 90 inclusive after the exam. This can be represented as a compound inequality:
80 ≤ (4/5) * 85 + (1/5) * x ≤ 90
To solve this inequality, we can simplify it:
80 ≤ (4/5) * 85 + (1/5) * x ≤ 90
80 ≤ (340/5) + (1/5) * x ≤ 90
80 ≤ 68 + (1/5) * x ≤ 90
12 ≤ (1/5) * x ≤ 22
To isolate "x" in the middle, we can multiply the inequality by 5:
5 * 12 ≤ 5 * (1/5) * x ≤ 5 * 22
60 ≤ x ≤ 110
Therefore, the possible score the student needs to make on the exam to get the desired average in the course is between 60 and 110 inclusive.
Let's assume the score the student needs on her exam is represented by 'x'.
The student's overall grade is determined by her class average (4/5) and her exam score (1/5).
To find the compound inequality, we can use the following equation:
80 ≤ (4/5)(class average) + (1/5)(exam score) ≤ 90
Substituting the given information, the equation becomes:
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) + (x/5) ≤ 90
To get rid of the denominators, we can multiply all parts of the inequality by 5:
5(80) ≤ 5(340/5) + 5(x/5) ≤ 5(90)
400 ≤ 340 + x ≤ 450
Next, we can simplify the inequality:
400 ≤ 340 + x ≤ 450
Subtract 340 from all parts of the inequality:
400 - 340 ≤ 340 - 340 + x ≤ 450 - 340
60 ≤ x ≤ 110
Therefore, the possible score the student needs to make on the exam to get the desired average in the course is between 60 and 110 inclusive.