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Answer :
To solve the problem of finding out how many two-point and four-point questions Tiffany answered, we need to set up a system of equations. Let's break it down step-by-step:
1. Define the Variables:
- Let [tex]\( t \)[/tex] represent the number of two-point questions.
- Let [tex]\( f \)[/tex] represent the number of four-point questions.
2. Set Up the Equations:
- Since the total number of questions is 42, we have:
[tex]\[
t + f = 42
\][/tex]
- Since the total number of points is 100, with each two-point question worth 2 points and each four-point question worth 4 points, the equation is:
[tex]\[
2t + 4f = 100
\][/tex]
3. Verify the Correct Equations:
By examining the problem statement and the requirements, it’s clear that these two equations represent the situation accurately:
- [tex]\( t + f = 42 \)[/tex] captures the total number of questions.
- [tex]\( 2t + 4f = 100 \)[/tex] captures the total points from these questions.
Therefore, the equations that accurately represent the scenario are [tex]\( t + f = 42 \)[/tex] and [tex]\( 2t + 4f = 100 \)[/tex].
These equations can be solved simultaneously to find the exact number of two-point and four-point questions, but based on the instructions provided, the focus is on establishing the correct equations rather than calculating a specific numeric solution.
1. Define the Variables:
- Let [tex]\( t \)[/tex] represent the number of two-point questions.
- Let [tex]\( f \)[/tex] represent the number of four-point questions.
2. Set Up the Equations:
- Since the total number of questions is 42, we have:
[tex]\[
t + f = 42
\][/tex]
- Since the total number of points is 100, with each two-point question worth 2 points and each four-point question worth 4 points, the equation is:
[tex]\[
2t + 4f = 100
\][/tex]
3. Verify the Correct Equations:
By examining the problem statement and the requirements, it’s clear that these two equations represent the situation accurately:
- [tex]\( t + f = 42 \)[/tex] captures the total number of questions.
- [tex]\( 2t + 4f = 100 \)[/tex] captures the total points from these questions.
Therefore, the equations that accurately represent the scenario are [tex]\( t + f = 42 \)[/tex] and [tex]\( 2t + 4f = 100 \)[/tex].
These equations can be solved simultaneously to find the exact number of two-point and four-point questions, but based on the instructions provided, the focus is on establishing the correct equations rather than calculating a specific numeric solution.
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