Answer :
Sure, let's work through the problem step-by-step.
We are given the following equations:
[tex]\[
\begin{array}{l|l}
T = 150c - 3 & T = -3c + 150 \\
\hline
T = -150c + 3 & T = 3c - 150
\end{array}
\][/tex]
### Step 1: Equate the first pair of equations
For the first pair:
[tex]\[ 150c - 3 = -3c + 150 \][/tex]
To solve for [tex]\( c \)[/tex], follow these steps:
1. Add [tex]\( 3c \)[/tex] to both sides to gather all terms involving [tex]\( c \)[/tex] on one side:
[tex]\[ 150c + 3c - 3 = 150 \][/tex]
2. Combine like terms:
[tex]\[ 153c - 3 = 150 \][/tex]
3. Add 3 to both sides to isolate the [tex]\( c \)[/tex]-term:
[tex]\[ 153c = 153 \][/tex]
4. Divide both sides by 153:
[tex]\[ c = 1 \][/tex]
### Step 2: Equate the second pair of equations
For the second pair:
[tex]\[ -150c + 3 = 3c - 150 \][/tex]
To solve for [tex]\( c \)[/tex], follow these steps:
1. Add [tex]\( 150c \)[/tex] to both sides to gather all terms involving [tex]\( c \)[/tex] on one side:
[tex]\[ 3 = 3c + 150c - 150 \][/tex]
2. Combine like terms:
[tex]\[ 3 = 153c - 150 \][/tex]
3. Add 150 to both sides to isolate the [tex]\( c \)[/tex]-term:
[tex]\[ 153 = 153c \][/tex]
4. Divide both sides by 153:
[tex]\[ c = 1 \][/tex]
### Final Answer
Both pairs of equations yield the solution:
[tex]\[ c = 1 \][/tex]
Thus, the value of [tex]\( c \)[/tex] that satisfies both sets of equations is [tex]\( c = 1 \)[/tex].
We are given the following equations:
[tex]\[
\begin{array}{l|l}
T = 150c - 3 & T = -3c + 150 \\
\hline
T = -150c + 3 & T = 3c - 150
\end{array}
\][/tex]
### Step 1: Equate the first pair of equations
For the first pair:
[tex]\[ 150c - 3 = -3c + 150 \][/tex]
To solve for [tex]\( c \)[/tex], follow these steps:
1. Add [tex]\( 3c \)[/tex] to both sides to gather all terms involving [tex]\( c \)[/tex] on one side:
[tex]\[ 150c + 3c - 3 = 150 \][/tex]
2. Combine like terms:
[tex]\[ 153c - 3 = 150 \][/tex]
3. Add 3 to both sides to isolate the [tex]\( c \)[/tex]-term:
[tex]\[ 153c = 153 \][/tex]
4. Divide both sides by 153:
[tex]\[ c = 1 \][/tex]
### Step 2: Equate the second pair of equations
For the second pair:
[tex]\[ -150c + 3 = 3c - 150 \][/tex]
To solve for [tex]\( c \)[/tex], follow these steps:
1. Add [tex]\( 150c \)[/tex] to both sides to gather all terms involving [tex]\( c \)[/tex] on one side:
[tex]\[ 3 = 3c + 150c - 150 \][/tex]
2. Combine like terms:
[tex]\[ 3 = 153c - 150 \][/tex]
3. Add 150 to both sides to isolate the [tex]\( c \)[/tex]-term:
[tex]\[ 153 = 153c \][/tex]
4. Divide both sides by 153:
[tex]\[ c = 1 \][/tex]
### Final Answer
Both pairs of equations yield the solution:
[tex]\[ c = 1 \][/tex]
Thus, the value of [tex]\( c \)[/tex] that satisfies both sets of equations is [tex]\( c = 1 \)[/tex].
