There are 80 questions on a college entrance examination. Two points are awarded for each correct answer, and one-half point is deducted for each incorrect answer. How many questions does Tami need to answer correctly in order to score at least 100 on the test? Assume that Tami answers every question.

If she gets x right, then she gets 80-x wrong. That means we need

2x - 1/2 (80-x) >= 100
5/2 x - 40 >= 100
5/2 x >= 140
x >= 56

2+2

Hey Steve, where did the 5/2 come from?

2x+1x/2

Common denominator
4x/2+1x/2

To figure out how many questions Tami needs to answer correctly in order to score at least 100 on the test, we need to use the scoring system given.

Let's assume that Tami answers all 80 questions.

For each correct answer, Tami receives 2 points, so if she answers all questions correctly, she would get 2 points * 80 questions = 160 points.

For each incorrect answer, Tami loses half a point, so if she answers all questions incorrectly, she would lose 0.5 points * 80 questions = 40 points.

Since Tami needs to score at least 100 on the test, we can set up the following inequality:

Total points >= 100

160 points - 40 points >= 100

120 points >= 100

Therefore, Tami needs to score at least 100 points, which means she needs to answer at least 100 / 2 = 50 questions correctly.

In conclusion, Tami needs to answer at least 50 questions correctly in order to score at least 100 on the test.