Problem:

Mary is taking an introductory algebra course in which four are to be given. To get an A, a student must average at least 90 on the four tests. Mary got scores of 96, 82 and 91 on the first three tests. Determine (in terms of an inequality) what scores on the last test will earn her an A.

Solution:

Step 1: Understand the problem:

Many students in Mary's situation might make a guess, like 87, and then compute the average of the four scores. The average of the four scores is their sum divided by the number of test, 4:

Step 2: Translate the problem into inequality.

Our work shows that an 87 will not earn Mary her A, since the average is not at least 90. Rather than make a second guess, let us translate the problem to an inequality. We let x be the Mary's score on the last test. Having familiarized ourselves with the meaning of average, we can reword and translate the problem into an inequality, using x as the fourth score.

Rewording:

The average of the four scores must be at least 90.

Step 3: Solve the problem which is the value of x using the inequality.

Checking:

Step 4: check, we can obtain a partial check by substituting a number greater than or equal to 91.

Answer:

∴ Therefore, the score is 91 or better on the last test will give Mary an A in the course.

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