Question

Your teacher is giving you a test worth 100 points that contains 40 questions. There are 2-point questions and 4-point questions on the test. Use 't' to represent 2-point questions and 'f' to represent 4-point questions. How many of each type of question are on the test?

A. t = 15, f = 25
B. t = 20, f = 20
C. t = 25, f = 15
D. t = 30, f = 10

Answer 1

By setting up a system of equations based on the total number of questions and the total points on the test, we find that there are 30 two-point questions and 10 four-point questions, making Option D (t = 30, f = 10) the correct answer.

Step-by-step explanation:

To solve the question of how many 2-point questions (t) and 4-point questions (f) are on a 100 point test with 40 questions, we need to set up a system of equations. First, we know that the total number of t and f must equal the total number of questions: t + f = 40. Second, we know that the value of the t questions (2 points each) plus the value of the f questions (4 points each) must equal the total points of the test: 2t + 4f = 100.

By simultaneously solving these equations, we find the number of each type of question:

• From the first equation, we can express f in terms of t: f = 40 - t.
• Substituting f into the second equation gives us 2t + 4(40 - t) = 100.
• Simplifying the equation, we get 2t + 160 - 4t = 100, which then becomes -2t = -60, leading to t = 30.
• Substituting t back into f = 40 - t gives us f = 40 - 30 = 10.

Therefore, Option D. t = 30, f = 10 is the correct answer.