Olivia is taking a test that has 30 questions.She earns 9 points for every correct answer and loses 5 points for every wrong answer (questions left blank also count as wrong answers) . If Olivia’s score is 18 , how many questions did she answer correctly on the test .

Question

Olivia is taking a test that has 30 questions.She earns 9 points for every correct answer and loses 5 points for every wrong answer (questions left blank also count as wrong answers) . If Olivia’s score is 18 , how many questions did she answer correctly on the test .

Answer 1

9 c - 5(30 - c) = 18 ... 14 c - 150 = 18

Answer 2

To find out how many questions Olivia answered correctly on the test, we can use algebra.

Let's assume that Olivia answered x questions correctly. Since there are 30 questions in total, she answered (30 - x) questions incorrectly or left them blank.

For every correct answer, Olivia earns 9 points, so her total score for correct answers would be 9x.

For every wrong answer or blank question, Olivia loses 5 points, so her total score for incorrect answers or blank questions would be 5 * (30 - x).

We know that her total score is 18, so we can set up the equation:

9x - 5 * (30 - x) = 18

Now, let's solve the equation.

9x - 150 + 5x = 18

Combining like terms:

14x - 150 = 18

Adding 150 to both sides:

14x = 168

Dividing both sides by 14:

x = 12

Therefore, Olivia answered 12 questions correctly on the test.