Cab companies often charge a flat fee for picking someone up and then an additional fee per mile driven. The city of Charlotte, NC charges a $2.50 fee and and $2.50 per mile for each can ride.
3. Write an equation in standard form to represent the amount charged, C, for m number of miles by the company in Charlotte. (Remember A cannot be negative and no fractions or decimals for any of the values)
The equation for the amount charged, C, for m number of miles would include the initial flat fee plus the charge per mile. This can be expressed as:
C = flat_fee + (charge_per_mile * m)
According to your information, the flat fee is $2.50 and the charge per mile is also $2.50. Substituting these values in yields:
C = 2.50 + (2.50 * m)
In standard form (Ax + By = C), we need to rearrange the equation so that all terms are on one side and we don't have any fractions or decimals. Since 'm' represents the number of miles and 'C' is the total charge, and considering that there is no 'B' or 'y' term in this linear equation, the equation simplifies to:
-2.50m + C = 2.50
Now, we're asked to ensure that there are no negative, fractional, or decimal values, meaning we need to eliminate the negative coefficient for 'm'. To do this, multiply the entire equation by -1 to get rid of the decimal and negative:
(2.50m) - C = -2.50
And then to put it in terms of whole numbers without decimals, we convert $2.50 into 250 cents (since $1 is equivalent to 100 cents). The equation becomes:
250m - C = -250
This is the standard form of the equation without negative, fractional, or decimal values, representing the amount charged, C, for m number of miles by the company in Charlotte, NC.