Question

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?

Answer 1

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 `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%`