Answer :
Sure! Let's solve the problem step-by-step.
We have two given equations for [tex]\( T \)[/tex]:
1. [tex]\( T = 150c - 3 \)[/tex]
2. [tex]\( T = -3c + 150 \)[/tex]
Our goal is to find the value of [tex]\( c \)[/tex] where both expressions for [tex]\( T \)[/tex] are equal.
First, set the two equations equal to each other:
[tex]\[ 150c - 3 = -3c + 150 \][/tex]
Next, combine like terms by adding [tex]\( 3c \)[/tex] to both sides:
[tex]\[ 150c + 3c - 3 = 150 \][/tex]
[tex]\[ 153c - 3 = 150 \][/tex]
To isolate the term with [tex]\( c \)[/tex], add 3 to both sides:
[tex]\[ 153c - 3 + 3 = 150 + 3 \][/tex]
[tex]\[ 153c = 153 \][/tex]
Now, solve for [tex]\( c \)[/tex] by dividing both sides by 153:
[tex]\[ c = \frac{153}{153} \][/tex]
[tex]\[ c = 1 \][/tex]
With [tex]\( c = 1 \)[/tex], substitute this value back into one of the original equations to find [tex]\( T \)[/tex]. We'll use the first equation:
[tex]\[ T = 150c - 3 \][/tex]
[tex]\[ T = 150(1) - 3 \][/tex]
[tex]\[ T = 150 - 3 \][/tex]
[tex]\[ T = 147 \][/tex]
So, the values are:
[tex]\[ c = 1 \][/tex]
[tex]\[ T = 147 \][/tex]
This means when [tex]\( c = 1 \)[/tex], we get [tex]\( T = 147 \)[/tex].
We have two given equations for [tex]\( T \)[/tex]:
1. [tex]\( T = 150c - 3 \)[/tex]
2. [tex]\( T = -3c + 150 \)[/tex]
Our goal is to find the value of [tex]\( c \)[/tex] where both expressions for [tex]\( T \)[/tex] are equal.
First, set the two equations equal to each other:
[tex]\[ 150c - 3 = -3c + 150 \][/tex]
Next, combine like terms by adding [tex]\( 3c \)[/tex] to both sides:
[tex]\[ 150c + 3c - 3 = 150 \][/tex]
[tex]\[ 153c - 3 = 150 \][/tex]
To isolate the term with [tex]\( c \)[/tex], add 3 to both sides:
[tex]\[ 153c - 3 + 3 = 150 + 3 \][/tex]
[tex]\[ 153c = 153 \][/tex]
Now, solve for [tex]\( c \)[/tex] by dividing both sides by 153:
[tex]\[ c = \frac{153}{153} \][/tex]
[tex]\[ c = 1 \][/tex]
With [tex]\( c = 1 \)[/tex], substitute this value back into one of the original equations to find [tex]\( T \)[/tex]. We'll use the first equation:
[tex]\[ T = 150c - 3 \][/tex]
[tex]\[ T = 150(1) - 3 \][/tex]
[tex]\[ T = 150 - 3 \][/tex]
[tex]\[ T = 147 \][/tex]
So, the values are:
[tex]\[ c = 1 \][/tex]
[tex]\[ T = 147 \][/tex]
This means when [tex]\( c = 1 \)[/tex], we get [tex]\( T = 147 \)[/tex].
