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River C is 200 miles longer than River D. If the sum of their lengths is 5,570 ​miles, what is the length of each​ river?

 Feb 11, 2021
 #1
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Please refrain from posting AMC problems.

 Feb 11, 2021
 #2
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what does that mean?

Guest Feb 11, 2021
 #3
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Let's make this into a system of equations. Our first equation is

River C + River D = $5,570$

Our second equation is

-River C + River D = $200$

We can find the length of River C by using the elimination method for a system of $2$ equations because River C in equation $2$ is negative and River C in equation $1$ is positive (postive + negative = elimination). We get:

   River C + River D = $5,570$

+ -River C + River D = $200$

_______________________

   2 * River D = $5,770$

To get rid of the $2$ we divide both sides by $2$ to get 

River D Length = $2885$

Now we can plug River D's Length into the first equation to get

River C + $2885$ = $5,570$

We subtract $2885$ from both sides to get 

River C Length = $2685$

So our answer's are River C = $2685$ & River D = $2885$!

NOTE: I was just reviewing this and realized I read the problem wrong I swaped the legnths for River C & D my bad. The real answers are:
River C = $2885$ & River D = $2685$

 Feb 11, 2021

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