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QuestionYou have grades 89, 78, and 83. If you score 100 on the final, what is your average? Can you get an A? What score is needed for a B?

Studdy Solution

STEP 1

Assumptions1. The grades for the first three examinations are89,78, and83. . The final examination counts as one grade.
3. To get an A, the average must be at least90.
4. To get a B, the average must be at least80.
5. The maximum possible grade on the final is100.

STEP 2

First, let's calculate the current average of the three examinations. The average is calculated by adding up all the grades and dividing by the number of grades.
Average=Sum of gradesNumber of gradesAverage = \frac{Sum\, of\, grades}{Number\, of\, grades}

STEP 3

Now, plug in the given values for the grades and the number of grades to calculate the current average.
Average=89+78+833Average = \frac{89 +78 +83}{3}

STEP 4

Calculate the current average.
Average=2503≈83.33Average = \frac{250}{3} \approx83.33

STEP 5

Now, let's calculate the final average if you get100 on the final examination. The final average is calculated by adding up all the grades (including the final) and dividing by the total number of grades.
Final average=Sum of grades+Final gradeTotal number of gradesFinal\, average = \frac{Sum\, of\, grades + Final\, grade}{Total\, number\, of\, grades}

STEP 6

Plug in the values for the sum of grades, the final grade, and the total number of grades to calculate the final average.
Final average=250+1004Final\, average = \frac{250 +100}{4}

STEP 7

Calculate the final average.
Final average=3504=87.5Final\, average = \frac{350}{4} =87.5So, even if you get100 on the final, your numerical average would be87.5, which is less than90. Therefore, an A in the course is not possible.

STEP 8

Now, let's find out what grade you must get on the final to earn a B in the course. We know that to get a B, the final average must be at least80. Let's denote the grade you must get on the final as x. We can set up the following equation80=250+x480 = \frac{250 + x}{4}

STEP 9

olve the equation for x.
80×4=250+x80 \times4 =250 + x320=250+x320 =250 + xx=320−250x =320 -250

STEP 10

Calculate the grade you must get on the final to earn a B in the course.
x=320−250=70x =320 -250 =70So, you must get at least70 on the final to earn a B in the course.

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