Question

Список заданий викторины состоял из 75 вопросов.  За каждый правильный ответ ученик получал 9 очков, за неправильный ответ с него списывали 16 очков, а при отсутствии ответа давали 0 очков. Сколько заданий оставил без ответа ученик, набравший 189 очков, если известно, что он ошибся по крайней мере 10 раз?​

Answer 1

Calculation of Unanswered Questions

To calculate the number of unanswered questions, we need to consider the scoring system provided. Each correct answer earns the student 9 points, each incorrect answer deducts 16 points, and a missing answer results in 0 points.

Let's assume the student answered x questions correctly, y questions incorrectly, and z questions were left unanswered.

According to the given information, we can set up the following equation:

9x - 16y + 0z = 189

We also know that the student made at least 10 mistakes, so y (the number of incorrect answers) is greater than or equal to 10.

Now, let's solve the equation to find the number of unanswered questions.

Solving the Equation

To solve the equation, we need to find the values of x, y, and z that satisfy the equation 9x - 16y + 0z = 189, with the condition that y is greater than or equal to 10.

Let's start by substituting y with 10 and solving for x:

9x - 16(10) = 189 9x - 160 = 189 9x = 189 + 160 9x = 349 x = 349 / 9 x ≈ 38.78

Since the number of questions cannot be a decimal, we can round down x to the nearest whole number, which is 38.

Now, let's substitute the values of x and y into the equation to find z:

9(38) - 16(10) + 0z = 189 342 - 160 + 0z = 189 182 + 0z = 189 0z = 189 - 182 0z = 7

Since any number multiplied by 0 is 0, we can conclude that z (the number of unanswered questions) is 7.

Answer

The student left 7 questions unanswered and scored a total of 189 points, with at least 10 incorrect answers.