alex’s can Company charges $1.00 plus an additional $3.00 per mile for a ride. madeleine’s company charges $3.00 plus an additional $2.00 per mile for a ride.

Question

write a system of linear equations that show the cost in dollars, Y, for a cab ride of X miles for each driver.

at what distance, in miles, will the cost be the same for both companies?

Answer 1

To write a system of linear equations, certain words are clues to which operation to perform. In this case "additional" means "+" and "per mile" means "x", with "y" already given as "cost in dollars".

$3.00 times (x) per mile plus the initial charge $1.00 = cost in dollars

$2.00 times (x) per mile plus the initial charge $3.00 = cost in dollars

Alex 3x + 1 = y

Madeleine 2x + 3 = y

To find out the same cost, set each linear equation equal to the other.

3x + 1 = 2x + 3

Solve for x (miles) by getting x on one side of the equal sign and all the numbers on the other.

3x - 2x = 3 - 1

Combine like terms and divide each side by 1.

Answer: x = 2 miles

Then check it by substituting 2 in for x in the two original linear equations.

Answer 2

They ask you to find miles, let it be x.

y1=3x+1

y2=2x+3

cost be the same for both companies, so

set y1=y2, this means,

3x+1=2x+3

solve to get x=2.

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