How many multiple-choice (x) and free-response (y) questions does Amy have to answer to earn 800 points? Provide 3 combinations of multiple-choice and free-response questions that result in 800 points.

Option 1: 10 MCQs and 75 free-response questions
Option 2: 30 MCQs and 50 free-response questions
Option 3: 40 MCQs and 40 free-response questions

Amy can earn 800 points by answering 10 multiple choice questions and 75 free response questions, 30 multiple choice questions and 50 free response questions, or 40 multiple choice questions and 40 free response questions.

Explanation:

Let x be the number of multiple choice questions and y be the number of free response questions.

We are given that 10x + 75y = 800, 30x + 50y = 800, 40x + 40y = 800, and 90x + 70y = 800.

One possible combination is x = 10 and y = 5, as it satisfies the first equation: 10(10) + 75(5) = 100 + 375 = 475. However, it does not satisfy the second equation.

Another possible combination is x = 20 and y = 4, as it satisfies the second equation: 30(20) + 50(4) = 600 + 200 = 800. However, it does not satisfy the first equation.

The third and final combination is x = 40 and y = 5, as it satisfies both the first and second equations: 10(40) + 75(5) = 400 + 375 = 775 and 30(40) + 50(5) = 1200 + 250 = 1450. Therefore, the three combinations are:

10 multiple choice questions and 75 free response questions
30 multiple choice questions and 50 free response questions
40 multiple choice questions and 40 free response questions

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