Question

A test has twenty-four questions and is worth a total of 100 points. The test consists of true/false questions worth 4 points each and multiple-choice questions worth 5 points each. How many true/false questions are on the test?

a) 12
b) 6
c) 8
d) 16

Answer 1

Using an algebraic equation, the number of true/false questions, represented as T, and the number of multiple-choice questions, represented as M, are calculated. However, the calculated result does not match the given answer options, indicating a possible error in the question or the options provided.

Step-by-step explanation:

To figure out how many true/false questions are on the test, we can set up an algebraic equation. Let's denote the number of true/false questions as T and the number of multiple-choice questions as M.

From the information given, we have two equations. The first one represents the total number of questions: T + M = 24. The second one represents the total points: 4T + 5M = 100.

Now we can solve these equations simultaneously to find the value of T. First, we can rearrange the first equation to get M = 24 - T. We then substitute this into the second equation to get 4T + 5(24 - T) = 100.

Simplifying that, we get 4T + 120 - 5T = 100, which simplifies further to -T = -20. So T = 20. Since there are 24 questions in total and 20 true/false questions, this means there must be 4 multiple-choice questions remaining. However, this solution does not match any of the provided options (a) 12 (b) 6 (c) 8 (d) 16. Therefore, there must be an error in the options given, or there might be a mistake in the provided details.