Question

A taxi ride in Test Guyville costs $5.00 plus a

variable fee directly proportional to the square
root of the number of miles traveled. If a 9-mile
taxi ride costs $9.50, how much does a 36-mile
ride cost?
A. $18
B. $23
C. $14
D. $11
E. $113

Answer 1

Let's set up an equation to solve this problem. We know that the cost of a taxi ride is $5.00 plus a variable fee directly proportional to the square root of the number of miles traveled. Let C be the total cost and M be the number of miles traveled.

So, we can write the equation as:

C = $5.00 + k√M

Where k is the constant of proportionality. We can find the value of k using the information given for the 9-mile taxi ride:

$9.50 = $5.00 + k√9

Now, solve for k:

$9.50 = $5.00 + 3k

3k = $9.50 - $5.00

3k = $4.50

k = $4.50 / 3

k = $1.50

Now that we have the value of k, we can find the cost of a 36-mile ride:

C = $5.00 + $1.50√36

C = $5.00 + $1.50 * 6

C = $5.00 + $9.00

C = $14.00

So, a 36-mile taxi ride costs $14. Therefore, the correct answer is C. $14.