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%#.

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 #2x# 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 + 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%#