Question 773216
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Josh wants to learn a minimum grade of an 85 this semester in algebra. His test and class work on average is an 82, this grade will count as 80% of his semester grade. His exam will be worth 100 points and will count as 20% of his total grade. Write and solve an inequality to determine what minimum grade Josh must make on his exam to earn an 85/B for his final grade. 
Ans:
Say he scores x/100 in the final exam.
The class work score of 82/100 carries 80% weightage. The final exam score (x/100)
will carry 20% weightage.
This is similar to saying that the final score is the sum of the scores in 2 tests
- class work test of 80 marks and final exam of 20 marks.
The overall grade of 85 is the sum of 2 scores:
1) Class work score with 80% weightage = 82 * 80* = 65.6. In other words, 
scoring 82/100 in the class test is the same as scoring 65.6/80 in the final
grade.
2) Final exam score with 20% weightage = (x)*20% = 0.2*x. In other words, 
scoring x/100 in the final test is the same as scoring 0.2*x in the final
grade.
Now the final grade is the sum of the 2, and has to be at least 85.
So you have the inequality
{{{65.6 + 0.2*x >= 85}}}
Simplifying
{{{0.2*x >= 19.4}}} or {{{x >= 97}}}
He has to score at least 97/100 or higher in the final exam to get an overall
grade of 85.
Hope you got it :)
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