Answer :
To solve the problem, we need to represent the relationship between Teresa's and Cathy's weights using a system of equations. Here's how we can break it down:
1. Define the Variables:
- Let [tex]\( T \)[/tex] represent Teresa's weight.
- Let [tex]\( C \)[/tex] represent Cathy's weight.
2. Understand the Relationships:
- We know that the sum of Teresa's and Cathy's weight is 118 pounds. This gives us the equation:
[tex]\[
T + C = 118
\][/tex]
- We also know that Teresa weighs 26 pounds more than Cathy. This gives us the second equation:
[tex]\[
T = C + 26
\][/tex]
3. Set Up the System of Equations:
- We combine the two pieces of information into a system of equations:
[tex]\[
\begin{cases}
T + C = 118 \\
T = C + 26
\end{cases}
\][/tex]
4. Identify the Correct Answer Option:
- Comparing the system of equations we have with the given options:
- Option A: Does not match because [tex]\( T = 26 \)[/tex] is incorrect.
- Option B: Incorrect because [tex]\( T + 26 = C \)[/tex] makes no sense in this context.
- Option C: The sum [tex]\( T + C = 64 \)[/tex] doesn't align with the information given.
- Option D: Incorrect setup of relations.
- Therefore, the correct system of equations is not present in the given options.
5. Conclusion:
The correct system of equations, based on the relationships described, should be:
[tex]\[
\begin{cases}
T + C = 118 \\
T = C + 26
\end{cases}
\][/tex]
Unfortunately, this option is not listed among the provided choices. Thus, the correct response is that none of the options fully represent the relationship, which would suggest the answer is:
E) None of the above.
1. Define the Variables:
- Let [tex]\( T \)[/tex] represent Teresa's weight.
- Let [tex]\( C \)[/tex] represent Cathy's weight.
2. Understand the Relationships:
- We know that the sum of Teresa's and Cathy's weight is 118 pounds. This gives us the equation:
[tex]\[
T + C = 118
\][/tex]
- We also know that Teresa weighs 26 pounds more than Cathy. This gives us the second equation:
[tex]\[
T = C + 26
\][/tex]
3. Set Up the System of Equations:
- We combine the two pieces of information into a system of equations:
[tex]\[
\begin{cases}
T + C = 118 \\
T = C + 26
\end{cases}
\][/tex]
4. Identify the Correct Answer Option:
- Comparing the system of equations we have with the given options:
- Option A: Does not match because [tex]\( T = 26 \)[/tex] is incorrect.
- Option B: Incorrect because [tex]\( T + 26 = C \)[/tex] makes no sense in this context.
- Option C: The sum [tex]\( T + C = 64 \)[/tex] doesn't align with the information given.
- Option D: Incorrect setup of relations.
- Therefore, the correct system of equations is not present in the given options.
5. Conclusion:
The correct system of equations, based on the relationships described, should be:
[tex]\[
\begin{cases}
T + C = 118 \\
T = C + 26
\end{cases}
\][/tex]
Unfortunately, this option is not listed among the provided choices. Thus, the correct response is that none of the options fully represent the relationship, which would suggest the answer is:
E) None of the above.
