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Answer :
To solve the problem, we need to determine the number of two-point and four-point questions on Tiffany's test based on the information given.
1. Understand the Problem:
- The test has a total of 42 questions.
- The test is worth 100 points in total.
- There are two types of questions:
- Two-point questions
- Four-point questions
2. Define Variables:
- Let [tex]\( t \)[/tex] represent the number of two-point questions.
- Let [tex]\( f \)[/tex] represent the number of four-point questions.
3. Set Up Equations:
- We know the total number of questions is 42. This gives us the first equation:
[tex]\[
t + f = 42
\][/tex]
- The total points available from all questions is 100. Assuming each two-point question gives 2 points and each four-point question gives 4 points, we create the second equation:
[tex]\[
2t + 4f = 100
\][/tex]
4. Summary of Equations:
- The system of equations we have is:
1. [tex]\( t + f = 42 \)[/tex]
2. [tex]\( 2t + 4f = 100 \)[/tex]
These equations accurately describe the scenario given in the problem. To solve for the exact numbers of each type, you would typically use methods for solving systems of equations, such as substitution or elimination. However, this setup gives you the correct equations needed to solve the problem.
1. Understand the Problem:
- The test has a total of 42 questions.
- The test is worth 100 points in total.
- There are two types of questions:
- Two-point questions
- Four-point questions
2. Define Variables:
- Let [tex]\( t \)[/tex] represent the number of two-point questions.
- Let [tex]\( f \)[/tex] represent the number of four-point questions.
3. Set Up Equations:
- We know the total number of questions is 42. This gives us the first equation:
[tex]\[
t + f = 42
\][/tex]
- The total points available from all questions is 100. Assuming each two-point question gives 2 points and each four-point question gives 4 points, we create the second equation:
[tex]\[
2t + 4f = 100
\][/tex]
4. Summary of Equations:
- The system of equations we have is:
1. [tex]\( t + f = 42 \)[/tex]
2. [tex]\( 2t + 4f = 100 \)[/tex]
These equations accurately describe the scenario given in the problem. To solve for the exact numbers of each type, you would typically use methods for solving systems of equations, such as substitution or elimination. However, this setup gives you the correct equations needed to solve the problem.
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