In your class, you have scores of 85, 84, 67, 92 on the first four of five tests. To get a grade of C, the average of the first five test scores must be greater than or equal to 70 and less than 80.

Solve an inequality to find the least score you can get on the last test and still earn a C.

What score do you need if the fifth test counts as two tests?

To find the least score you can get on the last test and still earn a C, let's solve the inequality.

Let x be the score you need on the last test.

For the average to be greater than or equal to 70 and less than 80, the sum of the scores for all five tests divided by 5 must satisfy the following inequality:

(85 + 84 + 67 + 92 + 2x) / 5 ≥ 70 and (85 + 84 + 67 + 92 + 2x) / 5 < 80

To simplify, multiply both sides of the inequality by 5 to eliminate the denominator:

85 + 84 + 67 + 92 + 2x ≥ 350 and 85 + 84 + 67 + 92 + 2x < 400

Combine like terms:

328 + 2x ≥ 350 and 328 + 2x < 400

Subtract 328 from both sides of the inequalities:

2x ≥ 22 and 2x < 72

Divide both sides of the inequalities by 2:

x ≥ 11 and x < 36

So, the least score you can get on the last test and still earn a C is 11.

70 ≤ (85+84+67+92+x)/5 ≤ 80

350 ≤ 85+84+67+92+x ≤ 400
350 ≤ 328+x ≤ 400
22 ≤ x ≤ 72

If the 5th test count double, then you have
70 ≤ (85+84+67+92+2x)/6 ≤ 80
Now finish it off as above