College

We appreciate your visit to Tiffany is taking a 42 question test worth 100 points The test includes two point and four point questions How many of each type of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Tiffany is taking a 42-question test worth 100 points. The test includes two-point and four-point questions. How many of each type of question are on the test?

Which equations represent the scenario, where [tex]t[/tex] represents the number of two-point questions and [tex]f[/tex] represents the number of four-point questions? Check all that apply.

A. [tex]t + f = 42[/tex]
B. [tex]t + f = 100[/tex]
C. [tex]2t + 4f = 42[/tex]
D. [tex]2t + 4f = 100[/tex]
E. [tex]4t + 2f = 100[/tex]

Answer :

Certainly! Let's break down the problem to find out how many two-point and four-point questions are on Tiffany's test.

1. Understanding the Problem:
- The test has a total of 42 questions.
- The entire test is worth 100 points.
- There are two types of questions: two-point questions and four-point questions.
- We need to find out how many of each type of question is on the test.

2. Define the Variables:
- Let [tex]\( t \)[/tex] be the number of two-point questions.
- Let [tex]\( f \)[/tex] be the number of four-point questions.

3. Set Up the Equations:
- Since the total number of questions is 42, we can write the equation:
[tex]\[
t + f = 42
\][/tex]
- Since the total points are 100, and each two-point question contributes 2 points and each four-point question contributes 4 points, we set up the equation:
[tex]\[
2t + 4f = 100
\][/tex]

4. Check the Equations:
- The equation [tex]\( t + f = 42 \)[/tex] represents the total number of questions.
- The equation [tex]\( 2t + 4f = 100 \)[/tex] represents the total number of points.

5. Identifying Correct Equations:
- Both [tex]\( t + f = 42 \)[/tex] and [tex]\( 2t + 4f = 100 \)[/tex] are correct representations of the problem.

Let's proceed with these equations to solve for [tex]\( t \)[/tex] and [tex]\( f \)[/tex].

6. Solving the Equations:
- From the first equation, express [tex]\( t \)[/tex] in terms of [tex]\( f \)[/tex]:
[tex]\[
t = 42 - f
\][/tex]
- Substitute [tex]\( t = 42 - f \)[/tex] into the second equation:
[tex]\[
2(42 - f) + 4f = 100
\][/tex]
- Simplify and solve for [tex]\( f \)[/tex]:
[tex]\[
84 - 2f + 4f = 100
\][/tex]
[tex]\[
2f = 16
\][/tex]
[tex]\[
f = 8
\][/tex]

7. Find the Value of [tex]\( t \)[/tex]:
- Substitute [tex]\( f = 8 \)[/tex] back into the equation [tex]\( t = 42 - f \)[/tex]:
[tex]\[
t = 42 - 8
\][/tex]
[tex]\[
t = 34
\][/tex]

Therefore, there are 34 two-point questions and 8 four-point questions on the test.

Thanks for taking the time to read Tiffany is taking a 42 question test worth 100 points The test includes two point and four point questions How many of each type of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada