Question

How to put the below college algebra word problem in a number equation?

A student needs a 90% or higher average for all his courses in order to receive an Academic Scholarship. He has not submitted his final paper in Freshman Composition.

He knows from his test scores that he will receive 84% in College Algebra, 85% in World History, and 85% in Introduction to Chemistry.

What grade should he earn in the Freshman Composition class to receive the Academic Scholarship?

Answer 1

The average is the sum of all of the individual items divided by the number of entries.

We are told that the individual items are the student's grades for:

`"College Algebra" + "World History" + "Introduction to Chemistry" + "Freshman Composition"`

Substitute the grades for each of the 3 known courses and substitute `x` for `"Freshman Composition"`:

`84% + 85% + 85% + x`

Because there are 4 grades, we divide the sum by 4:

`(84% + 85% + 85% + x)/4`

To receive the award, we want the average to be greater than or equal to 90%:

`(84% + 85% + 85% + x)/4 >= 90%`

Solve for x.

Multiply both sides by 4:

`84% + 85% + 85% + x >= 360%`

Subtract `84% + 85% + 85%` from both sides:

`x >= 360%- 84% - 85% - 85%`

`x >= 106%`

The student must obtain a grade of at least `106%`