# 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?

Apr 25, 2018

The student must get a 95%.

#### Explanation:

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 $2 x$ and the number of test scores will now be $6$.

(86% + 88% + 92% + 84% + (2x)%)/6

(350 + (2x)%)/6

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

(350 + (2x)%)/6= 90%

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

$350 + 2 x = 540$

Use additive inverse to isolate the variable term.
$\cancel{350} + 2 x \cancel{- 350} = 540 - 350$

$2 x = 190$

Divide by $2$ to isolate the variable.
$\frac{\cancel{2} x}{\cancel{2}} = \frac{190}{2}$

x=95%