To earn an A in a course, you must have a final average of at least 90%. On the first 4 exams, you have grades of 86%, 88%, 92%, and 84%. If the final exam is worth 2 grades, what must you get on the final to earn an A in the course?

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Answer 1 · 2018-04-25T23:55:36

The student must get a $95 %$ $95%$ .

Average or Mean is the sum of all values divided by the number of values.

Since the unknown value is worth two test scores the missing value will be $2 x$ $2x$ and the number of test scores will now be $6$ $6$ .

$\frac{86 % + 88 % + 92 % + 84 % + (2 x) %}{6}$ $(86% + 88% + 92% + 84% + (2x)%)/6$

$\frac{350 + (2 x) %}{6}$ $(350 + (2x)%)/6$

Since we would like a $90 %$ $90%$ for our final grade we set this equal to $90 %$ $90%$

$\frac{350 + (2 x) %}{6} = 90 %$ $(350 + (2x)%)/6= 90%$

Use the multiplicative inverse to isolate the variable expression.
$cancel6(350 + (2x)%)/cancel6= 90%*6$

$350 + 2x= 540$

Use additive inverse to isolate the variable term.
$cancel350 + 2x cancel(-350)= 540 - 350$

$2x=190$

Divide by $2$ to isolate the variable.
$(cancel2x)/cancel2 = 190/2$

$x=95%$