Rebecca has scored 81, 83, and 87 on her first three
exams in her math class. If the standard 70,80,90
scale is used for grades and the exams are equally
weighted, what must her score on the final exam, m
, be in order to:
Write the solution set as an algebraic inequality solved for
the variable.
Get at least a C average on exams?
Get at least a B average on exams?
Get at least an A average on exams?

You want to find the set of final exam scores Rebecca may get for a given grade average. Her scores so far are 81, 83, 87, and all are equally weighted.

Generic solution

Let m represent the exam score Rebecca must get for a final grade score of g. Then we have ...

(m +81 +83 +87)/4 ≥ g

m ≥ 4g -251 . . . . . . . . . . . multiply by 4 and subtract 251

C average

When g=70, we have ...

m ≥ 4(70) -251 = 29 . . . . . lower limit for C

When g=80, we have ...

m ≥ 4(80) -251 = 69 . . . . . upper limit for C, lower limit for B

For a C average, Rebecca must have 29 ≤ m < 69 on her final exam.

B average

When g=90, we have ...

m ≥ 4(90) -251 = 109 . . . . . upper limit for B, lower limit for A

For a B average, Rebecca must have 69 ≤ m < 109 on her final exam.

A average

For an A average, Rebecca must have 109 ≤ m on her final exam.