Nick is doing some math exercises on a website called Khon Academy. In Khon Academy, you have to get at least 70% of the problems in an exercise right in order to gain proficiency. So far, Nick answered one question, and he didn't get it right. Suppose he answers 75% of the following q questions correctly and gains proficiency in the exercise. Write an inequality in terms of q that models the situation.

Question

Nick is doing some math exercises on a website called Khon Academy. In Khon Academy, you have to get at least 70% of the problems in an exercise right in order to gain proficiency. So far, Nick answered one question, and he didn't get it right. Suppose he answers 75% of the following q questions correctly and gains proficiency in the exercise.  Write an inequality in terms of q that models the situation.

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. Nick needs to get at least 70% of the problems right to gain proficiency. He has already answered one question incorrectly. If he answers 75% of the next q questions correctly, we need to find out how many questions that would be and ensure it meets the 70% threshold.Calculate correct answers: Calculate the number of questions Nick will answer correctly out of the next q questions. Since Nick will answer 75% of the next q questions correctly, the number of correct answers will be 0.75q.Include previous question: Include the question Nick has already answered. Nick has answered one question incorrectly, so the total number of questions answered will be q + 1. The number of correct answers is still 0.75q.Set up proficiency inequality: Set up the inequality to represent the proficiency requirement. To gain proficiency, the number of correct answers must be at least 70% of the total number of questions answered. The inequality will be: 0.75q / (q + 1) ≥ 0.70Solve for minimum questions: Solve the inequality for q. To find the minimum number of questions q that Nick needs to answer to achieve proficiency, we need to solve the inequality: 0.75q ≥ 0.70(q + 1)Distribute 0.70: Distribute the 0.70 on the right side of the inequality. 0.75q ≥ 0.70q + 0.70Subtract to isolate q: Subtract 0.70q from both sides of the inequality to isolate q. 0.75q - 0.70q ≥ 0.70 0.05q ≥ 0.70Divide to solve for q: Divide both sides of the inequality by 0.05 to solve for q. q ≥ 0.70 / 0.05 q ≥ 14

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