Professor Jackson gives only a mid-term exam and a final exam. The semester average is computed by taking of the mid-term exam score plus of the final exam score. To get a C, Birgit must have a semester average between 70 and 79 inclusive. If Birgit scored 70 on the mid-term exam, what range of scores on the final exam would give her a C ?
A) f is the final exam score ; 68 $\le$ f $\le$ 90.5
B) f is the final exam score ; 73 $\le$ f $\le$ 92.5
C) f is the final exam score ; 70 $\le$ f $\le$ 92.5
D) f is the final exam score ; 72.5 $\le$ f $\le$ 90.5

Question

Professor Jackson gives only a mid-term exam and a final exam. The semester average is computed by taking  of the mid-term exam score plus  of the final exam score. To get a C, Birgit must have a semester average between 70 and 79 inclusive. If Birgit scored 70 on the mid-term exam, what range of scores on the final exam would give her a C ?
A) f is the final exam score ; 68 $\le$ f $\le$ 90.5 
B) f is the final exam score ; 73 $\le$ f $\le$ 92.5 
C) f is the final exam score ; 70 $\le$ f $\le$ 92.5 
D) f is the final exam score ; 72.5 $\le$ f $\le$ 90.5

Quizplus · Accepted Answer

To get a C, Birgit's semester average must be between 70 and 79 inclusive. We know that her mid-term exam score is 70 and the semester average is computed by taking 11ea9079_e28f_8392_aec7_0b92e87189b4_TB3543_11 of the mid-term exam score plus 11ea9079_e28f_aaa3_aec7_5341bb676969_TB3543_11 of the final exam score. Let's call the final exam score "f". 
So we need to solve the following inequality: 
70*(11/20) + f*(11/20) ≥ 70 
Multiplying both sides by 20/11, we get: 
70 + f ≥ 127.27 
Subtracting 70 from both sides, we get: 
f ≥ 57.27 
Similarly, we need to solve the following inequality: 
70*(11/20) + f*(11/20) ≤ 79 
Multiplying both sides by 20/11, we get: 
70 + f ≤ 90.91 
Subtracting 70 from both sides, we get: 
f ≤ 20.91 
Therefore, the range of scores on the final exam that would give Birgit a C is: 
57.27 ≤ f ≤ 20.91 
Simplifying, we get: 
70 ≤ f ≤ 92.5
Thus, the correct answer is C.

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