Question

A taxi company charges $2.80 for the 1st mile and $1.60 for each additional mile another taxi company charges $3.20 for the 1st mile and $1 50 for each additional mile the total cost, y, for X number of miles can be found in this system :y=1.60x+2.80y=1.50x+3.201.which method of solving systems of, substitution, or elimination are the equation set up for explain your reasoning.2. after how many miles will a taxi cost the same 3.how much did that ride cost

Answer 1

For 1), the best method we can use is substitution, since we already have everything in terms of x. Now, to find 2) and 3) we have to solve the system:

`\begin{gathered} y=1.60x+2.8 \\ y=1.50x+3.20 \\ \Rightarrow1.60x+2.8=1.50x+3.20 \end{gathered}`

Solving for x, we can find how many mlies will a taxi cost the same:

`\begin{gathered} 1.60x+2.80=1.50x+3.20 \\ \Rightarrow1.60x-1.50x=3.20-2.80 \\ \Rightarrow0.10x=0.40 \\ \Rightarrow x=(0.40)/(0.10)=4 \\ x=4 \end{gathered}`

Therefore, after 4 miles the taxi ride will cost the same. To find out how much that ride cost, we use the value of x in any equation to find y:

`\begin{gathered} y=1.60x+2.8 \\ \Rightarrow y=1.60(4)+2.80=6.40+2.80=9.20 \\ y=9.20 \end{gathered}`

Finally, we have that the ride costs $9.20