Question

Mrs. Simmons gave a history test worth 92 points. There were only two types of questions on it: 2-point true/false questions and 5-point fill-in-the-blank questions. If there were a total of 34 questions on the test, how many of them were true/false? How many were fill-in-the-blank?

Answer 1

To find the number of true/false questions and fill-in-the-blank questions on the history test, set up a system of equations and solve. There are 26 true/false questions and 8 fill-in-the-blank questions on the test.

Step-by-step explanation:

In order to find the number of true/false questions and fill-in-the-blank questions on the test, we need to set up a system of equations.

Let's let x represent the number of true/false questions and y represent the number of fill-in-the-blank questions.

We know that there are a total of 34 questions on the test, so x + y = 34.

We also know that the total number of points on the test is 92.

The true/false questions are worth 2 points each and the fill-in-the-blank questions are worth 5 points each, so 2x + 5y = 92.

To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we can solve for x in terms of y: x = 34 - y.

Substituting this expression for x into the second equation, we get 2(34 - y) + 5y = 92.

Simplifying this equation, we get 68 - 2y + 5y = 92.

Combining like terms, we get 3y = 24.

Dividing both sides by 3, we find that y = 8.

So there are 8 fill-in-the-blank questions on the test. To find the number of true/false questions, we can substitute this value of y back into one of the original equations.

Let's use x + y = 34. Substituting y = 8, we can solve for x: x + 8 = 34.

Subtracting 8 from both sides, we find that x = 26.

Therefore, there are 26 true/false questions and 8 fill-in-the-blank questions on the test.