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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

2 Answers

1 vote

Answer:

24 miles

Explanation:

User Jakoss
by
8.3k points
5 votes

Answer:

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.

User Nagendra
by
8.2k points

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