Professor Smith gives only a midterm exam and a final exam. The average is computed by taking 1/3 of the midterm exam score and 2/3 of the final exam score. To get a “C” or better students must have at least 70 semester average.
If Laura scored only a 59 on the midterm, what is the minimum score would she have to get on the final in order to get a C or better?
(1/3)(59) + (2/3)F ≥ 70
times 3
59 + 2F ≥ 210
2F ≥ 151
F ≥ 75.5
check: suppose she got 80
Final mark = (1/3)59 + (2/3)80= 73 , OK
suppose she got 75
Final mark = 59/3 + (2/3)(75 = 69.666... which is < 70
To determine the minimum score Laura would need on the final exam, we can use algebra to solve the equation.
Let's represent Laura's final exam score by the variable "F". According to the average computation formula, the average is calculated by taking 1/3 of the midterm score and 2/3 of the final exam score:
Average = (1/3) * Midterm + (2/3) * Final
We are looking for the minimum score Laura would need on the final exam to achieve a "C" or better, which is at least 70. Therefore, we can set up the equation:
70 ≤ (1/3) * 59 + (2/3) * F
To solve for F, we can start by simplifying the equation:
70 ≤ (59/3) + (2/3) * F
Next, we can subtract (59/3) from both sides of the equation:
70 - (59/3) ≤ (2/3) * F
To simplify further, we can find the common denominator by multiplying 3 to both sides:
(210 - 59) / 3 ≤ F
Now we have:
151/3 ≤ F
To get the minimum score Laura would need on the final exam, we can round up the value of F to the nearest whole number. Therefore, Laura would need to score at least 51 on the final exam in order to get a "C" or better.