Answer:
Initial Fee is $2.
Step-by-step explanation:
Given:
Stops Price (dollars)
3 6.50
7 12.50
11 18.50
Also Given:
The price of a train ticket consists of an initial fee plus a constant fee per stop.
So let the Cost of initial fee be 'x'.
Also Let the Cost of Constant fee be 'y'.
Now Equation can framed as;
[tex]Price (P) = x + (y\times \textrm{Number of Stops})[/tex]
Now According to table;
Number of stops = 3
Price = 6.50
So equation can be framed as;
[tex]x+3y =6.50 \ \ \ \ equation \ 1[/tex]
Also According to table;
Number of stops = 7
Price = 12.50
So equation can be framed as;
[tex]x+7y =12.50 \ \ \ \ equation \ 2[/tex]
Now Subtracting equation 1 from equation 2 we get;
[tex](x+7y)-(x+3y) =12.50-6.50\\\\x+7y-x-3y=6\\\\4y =6\\\\y= \frac{6}{4}=\$1.5[/tex]
Substituting the value of y in equation 1 we get;
[tex]x+3\times1.5=6.50\\\\x+4.5=6.50\\\\x =6.50-4.5 = \$2[/tex]
Hence Initial Fee is $2.
