Question

A test has 30 questions worth 100 points. The test consists of true/false questions worth 3 points each and essay questions worth 5 points each. How many of each type of question is on the test?

A) Write equations and solve
B) Skip
C) Provide the solution
D) Write "Test Questions"

Answer 1

The test has 25 true/false questions and 5 essay questions. By setting up a system of equations that reflects the total number of questions and the total points, we can use the elimination method to find the number of each type of question.

Step-by-step explanation:

To determine the number of true/false and essay questions on the test, we can set up two equations using the given information. Let T represent the number of true/false questions and E represent the number of essay questions. The total number of questions is 30, which gives us our first equation:

Equation 1: T + E = 30

Next, we know that the true/false questions are worth 3 points each, and the essay questions are worth 5 points each, totaling 100 points. This gives us our second equation:

Equation 2: 3T + 5E = 100

To solve the system of equations, we can use the substitution or elimination method. Here we'll use the elimination method:

1. Multiply Equation 1 by 3 to align the coefficients with those of Equation 2: 3T + 3E = 90
2. Subtract this new equation from Equation 2 to eliminate T: (3T + 5E) - (3T + 3E) = 100 - 90, which simplifies to 2E = 10.
3. Divide by 2 to solve for E: E = 5. We have 5 essay questions.
4. Substitute the value of E back into Equation 1 to find T: T + 5 = 30, which simplifies to T = 25. We have 25 true/false questions.

Therefore, the test consists of 25 true/false questions and 5 essay questions.