Respuesta :
Answer:
Route y= 31 miles.
Route x= 24 miles.
Step-by-step explanation:
We have been given that each week Dan drives two routes: route x and route y.
One week he drives route x three times and route y 2 times. He drives a total of 134 miles that week. We can represent this information as: [tex]3x+2y=134..(1)[/tex]
Another week he drives route x twice and route y 5 times. He drives a total of 203 miles.We can represent this information as: [tex]2x+5y=203..(2)[/tex]
Upon using our given information we have formed a system of equations. Now we will solve our system of equations using substitution method.
From equation 1 we will get,
[tex]x=\frac{134-2y}{3}[/tex]
Upon substituting this value in 2nd equation we will get,
[tex]2(\frac{134-2y}{3})+5y=203[/tex]
Upon distributing 2 we will get,
[tex](\frac{268-4y}{3})+5y=203[/tex]
Now we will find a common denominator for left side of our equation.
[tex]\frac{268-4y+15y}{3}=203[/tex]
[tex]\frac{268+11y}{3}=203[/tex]
Upon multiplying both sides of our equation by 3 we will get,
[tex]268+11y=3\times 203[/tex]
[tex]268+11y=609[/tex]
[tex]11y=609-268[/tex]
[tex]11y=341[/tex]
[tex]y=\frac{341}{11}=31[/tex]
Therefore, the length of route y is 31 miles.
Now let us substitute y=31 in 1st equation to find the value of x.
[tex]3x+2\times 31=134[/tex]
[tex]3x+62=134[/tex]
[tex]3x=134-62[/tex]
[tex]3x=72[/tex]
[tex]x=\frac{72}{3}=24[/tex]
Therefore, the length of route x is 24 miles.
