Question

The following image contains the problem I have.please help its urgent.(will give good review)

Answer 1

`\begin{gathered} First\: car\colon35\: gallons \\ Second\: car\colon25\: gallons \end{gathered}`

1) We can solve this problem, using a linear system of equations. So, let's start out writing the equations from the problem, calling the first car a and the second car b

`\begin{gathered} 35a+20b=1725 \\ a+b=60 \end{gathered}`

The first equation refers to the consumption in gallons and the second, the consumption in gallons number of miles altogether.

2) So now, let's solve this system by the method of Elimination:

`\begin{gathered} \\ 35a+20b=1725\text{ } \\ a+b=60*(-35) \\ 35a+20b=1725 \\ -35a-35b=-2100 \\ ------------- \\ -15b=-375 \\ -(15b)/(-15)=-(375)/(-15) \\ b=25 \end{gathered}`

Now let's plug into the second and simplest equation b=35 to get a:

`\begin{gathered} a+25=60 \\ a+25-25=60-25 \\ a=35 \end{gathered}`