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.
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
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