Question

Marcus wants to end the semester with at least an 85 test average in his math class. On his first 3 tests, he earned 83, 97, and 80. What will he have to earn on his fourth test to have at least an 85 average? Let g represent the grade needed on his fourth test.

Write an inequality that models the situation.

Solve the inequality, and then explain what the solution means.

Answer 1

Explanation:

We know that Marcus wants to end the semester with at least an 85 test average in his math class. We can find the average of his first three test scores by adding them up and dividing by 3:

(83 + 97 + 80) / 3 = 86.67

So currently, Marcus has an average of 86.67. Let g represent the grade he needs on his fourth test to reach his goal of an 85 average.

To find the inequality, we can use the formula for the average of four numbers:

(83 + 97 + 80 + g) / 4 ≥ 85

This inequality states that the average of the four test scores (including the unknown fourth score, g) must be greater than or equal to 85.

Now we can solve for g:

(83 + 97 + 80 + g) / 4 ≥ 85

260 + g ≥ 340

g ≥ 80

This means that Marcus must earn at least an 80 on his fourth test to achieve an average of 85 or higher for the semester.

In other words, if Marcus earns an 80 or higher on his fourth test, he will achieve his goal of an 85 or higher average for the semester. If he earns less than an 80, his average for the semester will be less than 85.