math word problem

Question

In a large city, taxicabs charge $4.00 for the first 1/5 mile and $0.32 for each additional 1/5 mile.  Frank has only $7.50.  What is the maximum distance he can travel (not including a tip for the cabbie)?

Answer 1

It is very important to translate a word (story) problem into math variables and symbols correctly.  After that, the rules of math make solving the problem fairly easy.

Since taxicabs in the problem only charge for each 1/5 mile, we will write the formula using fifths of a mile and give the answer in fifths of a mile (rounding down if necessary).

 

Let x = number of fifths of a mile Frank travels

 

Translate:

  “taxicabs charge $4.00 for the first 1/5 mile and $0.32 for each additional 1/5 mile”     means

          charge      =        $4.00                            +      $0.32 * (x-1)

  “ Frank has only $7.50”      means

          charge <= $7.50

 

The math:

      $4.00 + $0.32(x-1)  <=  $7.50

      $4.00 + $0.32x - $0.32  <=  $7.50              [distribute]

      $3.68 + $0.32x  <=  $7.50                    [collect like terms]

       $0.32x  <=  $3.82               [subtract +$3.82 from both sides retains sense of inequality]

        x <= 11.93                [divide both sides by +$0.32 retains sense of inequality]

        x = 11        [remember, we must round down to a fifth of a mile]

 

Frank may travel a maximum of 11/5 mile  (that is, 2 1/5 miles).  

      [note: cost= $7.20;  for 2 2/5 miles, the cost would be $7.52]

Answer 2

Mary, let's let x = the number of 1/5 miles Frank can travel.

 

Then, we have...

 

4.00 + .32x < 7.50

            .32x < 3.50

                 x < 10.94

 

Since the taxi only charges in whole amounts, we round down to 10.

 

10(1/5) = 2.

 

Frank can travel 2 miles with his $7.50.

 

Hope this helps!