To solve this problem, let's start by identifying the given information and formulating the linear equation.
The charges are composed of:
- A flat pickup fee of [tex]$2.50.
- An additional charge of $[/tex]1.95 per mile.
If [tex]$x$[/tex] represents the number of miles driven, the total fare Isaac was charged can be expressed by the equation:
[tex]\[ 1.95x + 2.50 = 27.46 \][/tex]
Now, we need to solve for [tex]\( x \)[/tex] to find out how many miles Isaac traveled.
### Step-by-Step Solution:
1. Formulate the equation:
[tex]\[ 1.95x + 2.50 = 27.46 \][/tex]
2. Isolate the variable [tex]\( x \)[/tex] by first subtracting the flat fee from both sides:
[tex]\[ 1.95x = 27.46 - 2.50 \][/tex]
3. Calculate the right-hand side:
[tex]\[ 1.95x = 24.96 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by the per-mile charge [tex]\( 1.95 \)[/tex]:
[tex]\[ x = \frac{24.96}{1.95} \][/tex]
5. Perform the division to find [tex]\( x \)[/tex]:
[tex]\[ x = 12.8 \][/tex]
Thus, the linear equation used to solve this problem is:
[tex]\[ 1.95x + 2.50 = 27.46 \][/tex]
And Isaac traveled [tex]\( 12.8 \)[/tex] miles, rounded to the nearest tenth.
Therefore, the correct option is:
[tex]\[ 1.95 x + 2.50 = 27.46; \text{Isaac traveled 12.8 miles.} \][/tex]
