city taxi: $5.00 for the first mile and $2.25 for each additional mile metro taxi: $3.00 for the first mile and $2.50 for each additional mile

Question

For how many additional miles and how many total miles would the charge be the at each company

 

Answer 1

Hi Ryliegh Joy--

 

So you'll set up an equation that uses both companies at once. I'm going to turn the dollar amounts into cents because I hate decimals. :-)

 

The first company charges 225x + 500.  That's because the first mile is 500 cents (5 bucks) no matter what, and 225 cents more for each added mile. (Some number of miles that we're calling x for now.)

 

Second company charges 250x for the added miles + 300 for the first mile no matter what.

 

Those 2 price plans match each other when each taxi has gone "x" miles. SOO...

 

225x + 500 = 250x + 300

 

Get all the x terms on one side, and all the plain old normal numbers on the other, by subtracting 225x from each side AND subtracting 300 from each side.

 

That leaves you with 200 = 25x.  Which means that one little x is worth 8.

 

SOO, after the first mile and then 8 more miles (for a total of 9 miles), the cost will be the same no matter which company you choose.

 

Hope this helps!

 

Matt in NY

Answer 2

Let's say you choose the $3....................simultaneously........Let's virtually track the progress of your

for the first mile taxi and........................group member, who took the $5 taxi:

track your progress:..............................

Let's start at (1,3) which represents.........Let's start at (1,5) which represents a

a distance of 1 mile on the odometer.......a distance of 1 mile on the odometer

at a cost of $3, and track down...............at a cost of $5, and track down

where we are at after 9 increments:.......where we are at after 9 increments:

 

from the point (1,3), in increments of......from the point (1,5), in increments of 

1 mile and $2.50 we go to ....................1 mile and $2.25 we go to ....

(2, 5.5  ), for the first increment,...........(2, 7.25 ), for the first increment,

(3, 8     ), for the second  increment,.....(3, 9.5   ), for the second increment,

(4, 10.5), for the third      increment,.....(4, 11.75), for the third increment,

(5, 13   ), for the fourth    increment,.....(5, 14    ), for the fourth increment,

(6, 15.5), for the fifth       increment,.....(6, 16.25), for the fifth increment,

(7, 18   ), for the sixth     increment,......(7, 18.5   ), for the sixth increment,

(8, 20.5), for the seventh increment,......(8, 20.75 ), for the seventh increment,

(9, 23   ), for the eighth   increment,......(9, 23     ), for the eighth increment,

(10,25.5), for the ninth     increment......(10,25.25), for the ninth increment.

 

So starting at one mile, and already.......So starting at one mile, and already

having paid 3 dollars, you went 8 ..........having paid 5 dollars, you went 8

increments corresponding to 8 miles......increments corresponding to 8 miles

and paid $2.50 for each of the eight.......and paid $2.25 for each of the eight

increments.  So in addition to the...........increments. So in addition to the

first mile for $3, you went another..........first mile for $5, you went another

8 miles and paid (8 times $2.50),...........8 miles and paid (8 times $2.25),