Answer :
To solve this problem, we will set up a system of equations based on the information provided.
1. Identify Variables:
- Let [tex]\( T \)[/tex] be Teresa's weight.
- Let [tex]\( C \)[/tex] be Cathy's weight.
2. Set Up Equations:
- Equation 1: The sum of Teresa's and Cathy's weight is 118 pounds. This can be expressed as:
[tex]\[
T + C = 118
\][/tex]
- Equation 2: Teresa weighs 26 pounds more than Cathy. This can be expressed as:
[tex]\[
T = C + 26
\][/tex]
3. System of Equations:
- The system of equations is:
[tex]\[
\begin{align*}
T + C &= 118 \\
T &= C + 26
\end{align*}
\][/tex]
4. Solve the System of Equations:
- Substitute Equation 2 into Equation 1:
[tex]\[
(C + 26) + C = 118
\][/tex]
- Combine like terms:
[tex]\[
2C + 26 = 118
\][/tex]
- Subtract 26 from both sides:
[tex]\[
2C = 92
\][/tex]
- Divide both sides by 2 to solve for [tex]\( C \)[/tex]:
[tex]\[
C = 46
\][/tex]
- Use the value of [tex]\( C \)[/tex] to find [tex]\( T \)[/tex] using Equation 2:
[tex]\[
T = 46 + 26
\][/tex]
- Simplify to find [tex]\( T \)[/tex]:
[tex]\[
T = 72
\][/tex]
5. Conclusion:
- Cathy weighs 46 pounds.
- Teresa weighs 72 pounds.
Therefore, the correct system of equations that represents Teresa's and Cathy's weights is:
[tex]\[
\begin{align*}
T + C &= 118 \\
T &= C + 26
\end{align*}
\][/tex]
These correspond to the system in choice E, as none of the choices A, B, C, or D match exactly.
1. Identify Variables:
- Let [tex]\( T \)[/tex] be Teresa's weight.
- Let [tex]\( C \)[/tex] be Cathy's weight.
2. Set Up Equations:
- Equation 1: The sum of Teresa's and Cathy's weight is 118 pounds. This can be expressed as:
[tex]\[
T + C = 118
\][/tex]
- Equation 2: Teresa weighs 26 pounds more than Cathy. This can be expressed as:
[tex]\[
T = C + 26
\][/tex]
3. System of Equations:
- The system of equations is:
[tex]\[
\begin{align*}
T + C &= 118 \\
T &= C + 26
\end{align*}
\][/tex]
4. Solve the System of Equations:
- Substitute Equation 2 into Equation 1:
[tex]\[
(C + 26) + C = 118
\][/tex]
- Combine like terms:
[tex]\[
2C + 26 = 118
\][/tex]
- Subtract 26 from both sides:
[tex]\[
2C = 92
\][/tex]
- Divide both sides by 2 to solve for [tex]\( C \)[/tex]:
[tex]\[
C = 46
\][/tex]
- Use the value of [tex]\( C \)[/tex] to find [tex]\( T \)[/tex] using Equation 2:
[tex]\[
T = 46 + 26
\][/tex]
- Simplify to find [tex]\( T \)[/tex]:
[tex]\[
T = 72
\][/tex]
5. Conclusion:
- Cathy weighs 46 pounds.
- Teresa weighs 72 pounds.
Therefore, the correct system of equations that represents Teresa's and Cathy's weights is:
[tex]\[
\begin{align*}
T + C &= 118 \\
T &= C + 26
\end{align*}
\][/tex]
These correspond to the system in choice E, as none of the choices A, B, C, or D match exactly.
