If a student achieves an average exam score between 70 and 79, he will earn a grade of C in his algebra course. Suppose he has three exam scores of 75, 63, and 84 and that his teacher said the final exam score has twice the weight of the other three exams. What range of scores on the final exam will result in him earning a grade of C?
Accepted Solution
A:
Answer:Between 64 and 86.5 Step-by-step explanation:Let:w=weight of the first three exams.W=weight of the final exam.Now, the sum of the weight of the four exams must be 100, besides we know that W=2w, hence:[tex]w+w+w+W=100\\w+w+w+2w=100\\5w=100\\w=\frac{100}{5}=20[/tex]So, each exam has a weight of 20% and the final exam would have a weight of 40%. Let's calculate the average score in order to get at leats 70:Let:x=Minimun score to earn a C[tex]75*(\frac{20}{100} )+63*(\frac{20}{100} )+84*(\frac{20}{100} )+x*(\frac{40}{100} )=70[/tex]Solving for x:[tex]x=\frac{70-(44.4)}{0.4} =64[/tex]Finally, let's calculate the average score in order to get 84:Let:y=Maximun score to earn a C:[tex]75*(\frac{20}{100} )+63*(\frac{20}{100} )+84*(\frac{20}{100} )+y*(\frac{40}{100} )=79[/tex]Solving for y:[tex]y=\frac{79-(44.4)}{0.4} =86.5[/tex]