Question

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. Another week he drives route x twice and route y 5 times. He drives a total of 203 miles. Find the length of each route

Answer 1

Answer:

24 miles

Step-by-step explanation:

Answer 2

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: $3x+2y=134..(1)$  

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: $2x+5y=203..(2)$

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,

$x=\frac{134-2y}{3}$

Upon substituting this value in 2nd equation we will get,

$2(\frac{134-2y}{3})+5y=203$

Upon distributing 2 we will get,

$(\frac{268-4y}{3})+5y=203$

Now we will find a common denominator for left side of our equation.

$\frac{268-4y+15y}{3}=203$

$\frac{268+11y}{3}=203$

Upon multiplying both sides of our equation by 3 we will get,

$268+11y=3\times 203$

$268+11y=609$

$11y=609-268$

$11y=341$

$y=\frac{341}{11}=31$

Therefore, the length of route y is 31 miles.

Now let us substitute y=31 in 1st equation to find the value of x.

$3x+2\times 31=134$

$3x+62=134$

$3x=134-62$

$3x=72$

$x=\frac{72}{3}=24$

Therefore, the length of route x is 24 miles.