Answer :
To solve the problem of finding how many two-point and four-point questions are on Tiffany's test, we need to set up a system of equations based on the information given.
### Step-by-Step Solution:
1. Identify 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:
- Equation 1: We know the total number of questions is 42. Therefore, the sum of two-point and four-point questions is 42:
[tex]\[
t + f = 42
\][/tex]
- Equation 2: We also know the total points for the test is 100. Since two-point questions contribute 2 points each and four-point questions contribute 4 points each, the total points can be expressed as:
[tex]\[
2t + 4f = 100
\][/tex]
3. Review the Possible Equations:
- We have been given several options to consider:
- [tex]\( t + f = 42 \)[/tex]
- [tex]\( t + f = 100 \)[/tex]
- [tex]\( 2t + 4f = 42 \)[/tex]
- [tex]\( 2t + 4f = 100 \)[/tex]
- [tex]\( 4t + 2f = 100 \)[/tex]
4. Select the Correct Equations:
- From our setup, the correct equations that represent the scenario are:
- [tex]\( t + f = 42 \)[/tex]
- [tex]\( 2t + 4f = 100 \)[/tex]
These equations correctly model the situation, indicating the relationship between the number of questions and their total contribution to both the number of questions and the total points of the test.
### Step-by-Step Solution:
1. Identify 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:
- Equation 1: We know the total number of questions is 42. Therefore, the sum of two-point and four-point questions is 42:
[tex]\[
t + f = 42
\][/tex]
- Equation 2: We also know the total points for the test is 100. Since two-point questions contribute 2 points each and four-point questions contribute 4 points each, the total points can be expressed as:
[tex]\[
2t + 4f = 100
\][/tex]
3. Review the Possible Equations:
- We have been given several options to consider:
- [tex]\( t + f = 42 \)[/tex]
- [tex]\( t + f = 100 \)[/tex]
- [tex]\( 2t + 4f = 42 \)[/tex]
- [tex]\( 2t + 4f = 100 \)[/tex]
- [tex]\( 4t + 2f = 100 \)[/tex]
4. Select the Correct Equations:
- From our setup, the correct equations that represent the scenario are:
- [tex]\( t + f = 42 \)[/tex]
- [tex]\( 2t + 4f = 100 \)[/tex]
These equations correctly model the situation, indicating the relationship between the number of questions and their total contribution to both the number of questions and the total points of the test.
