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

24 miles

Explanation:

Answer 2

Route y= 31 miles.

Route x= 24 miles.

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=(134-2y)/(3)`

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

`2((134-2y)/(3))+5y=203`

Upon distributing 2 we will get,

`((268-4y)/(3))+5y=203`

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

`(268-4y+15y)/(3)=203`

`(268+11y)/(3)=203`

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

`268+11y=3* 203`

`268+11y=609`

`11y=609-268`

`11y=341`

`y=(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* 31=134`

`3x+62=134`

`3x=134-62`

`3x=72`

`x=(72)/(3)=24`

Therefore, the length of route x is 24 miles.