Question

Steve has these score on the exams for this semester: 89, 92, and 87. How much will have to make on the fourth exam to have a final average of an A (a 92% or better)?
A. 100%
B. 98% or better
C. 96% or better
D. 90% or better

Answer 1

268 + x ≥ 92*4

x ≥ 368 - 268

x ≥ 100

Answer 2

A is your answer

Answer 3

100% add them all together

Answer 4

and divide by 4

Answer 5

so the correct answer would be A. correct?

Answer 6

yes

Answer 7

There are two ways to go about a problem like this. One uses the formula for averages to solve for the exam score needed, and the other uses understanding of how averages are made to figure out how many points need to be made up with the exam.

The first method:
The average of the 4 exams is found by taking the sum of all the scores and dividing by the number of exams, 4. We don't know the 4th score yet, so we'll use x.
\[\frac{ 89 + 92 + 87 + x }{ 4} \ge 92\]
Simplifying:
\[268 + x \ge 368\]
So \[x \ge 100\]

The second method:
We want an average of at least 92. The simplest way to get that average is for each of the 4 scores to be 92. Since they're not, we look to see how far off they are to figure out how many points we need to make up.
92 is spot on, so 0 points there.
89 is 3 points short.
87 is 5 points short.
The total number of points we need to make up is 3 + 5 = 8. Since we're looking to get a 92, we add those 8 points to that score, giving us 100.

Either way, the answer is A.

Answer 8

@mslano thanks that makes more sense :)