There are 72 questions on a college entrance examination. One point is awarded for each correct answer, and one third of a one third of a point is deducted for each incorrect answer. How many questions does Tami need to answer correctly in order to score at least 60 points on the test? Assume that she answers every question.

Question

There are 72 questions on a college entrance examination. One point is awarded for each correct answer, and one third of a one third of a point is deducted for each incorrect answer. How many questions does Tami need to answer correctly in order to score at least 60 points on the test? Assume that she answers every question.

Answer 1

"one third of a one third of a point is deducted"

- why not just say say: " 1/9 of a point is deducted for an incorrecte answer" ??

number correct --- x
number incorrect --- 72-x

x - (1/9)(72-x) ≥ 60

x - 8 + (1/9)x ≥ 60
(10/9)x ≥ 68
x ≥ 61.2

So Tami must answer at least 62 correctly.

check:
with 61 correct:
score = 61 - (1/9)(11) = 59.78
with 62 correct
score = 62 - (1/9)(10) = 60.89 which is ≥ 60

Answer 2

it is incorrect, can u please help me see why?

Answer 3

probably because the 1/3 of 1/3 is a typo.

If you discount the stuttering, you have

x - (1/3)(72-x) ≥ 60

Solve that and see what you get. If it works, next time check the solution and see whether it interprets your problem correctly, instead of just blindly accepting the answer.

Answer 4

To calculate the number of questions Tami needs to answer correctly, we need to consider the scoring system of the test. Each correct answer earns a student one point, while each incorrect answer results in a deduction of one third of a one third of a point.

Step 1: Calculate the total score deduction for incorrect answers.
Since each incorrect answer results in a deduction of one third of a one third of a point, we can calculate the total point deduction by multiplying the number of incorrect answers by one third of a one third of a point. Given that Tami answers every question, we can find the number of incorrect answers by subtracting the number of correct answers from the total number of questions.

Number of incorrect answers = Total number of questions - Number of correct answers

Step 2: Calculate the total score.
The total score can be calculated by multiplying the number of correct answers by one point and subtracting the total point deduction for incorrect answers.

Total score = Number of correct answers * 1 point - Total point deduction for incorrect answers

Step 3: Determine the number of questions Tami needs to answer correctly.
To determine the number of questions Tami needs to answer correctly in order to score at least 60 points on the test, we need to solve the following inequality:

Number of correct answers ≥ (60 + Total point deduction for incorrect answers) / 1 point

Now let's calculate it step by step.

Step 1: Calculate the total score deduction for incorrect answers.
Since one third of a one third of a point is equal to (1/3) * (1/3), we can calculate the total point deduction for incorrect answers using the following formula:

Total point deduction for incorrect answers = (Number of incorrect answers) * (1/3) * (1/3)

Step 2: Calculate the total score.
The total score can be calculated using the following formula:

Total score = Number of correct answers - Total point deduction for incorrect answers

Step 3: Determine the number of questions Tami needs to answer correctly.
To score at least 60 points on the test, Tami needs to answer at least (60 + Total point deduction for incorrect answers) questions correctly.