Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run? The domain of the solution is . (a) Define your variable. (b) Write algebraic expressions for the distances each person ran. (c) Write an equation that can help you solve the problem. (d) Solve the equation. (e) Check your answer.

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Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run? The domain of the solution is . (a) Define your variable. (b) Write algebraic expressions for the distances each person ran. (c) Write an equation that can help you solve the problem. (d) Solve the equation. (e) Check your answer.

Mathematics
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im here
okay, lets see

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lets start with a
the answers a?
no, we have to do a-e in steps
lets do step a
oh ok go on..
Define the variable
let me write it out
ok
do 26-4 and then divide by two to get 11 miles
are you sure it is to divide by two?
let steve run x miles Kevin runes x + 4 so together they run 26 x + x+4 = 26 or 2x + 4 = 26 now solve for x
for x + x+4 = 26 and 2x + 4 = 26
no if you have the 2 distance x and x + 4 when you collect like terms it becomes 2x + 4 = 26 this is the only equation to solve
11 miles
great that's the number of miles run by who... Steve or Kevin...? to check go back to the variable definitions...
steve
great so since Kevin runs 4 miles more he runs 15 and part d asked you to check to solution 11 + 15 =26 so it works...
yep... and if you just subtract the distance between each other from the sum of their total distances you will get double Steve's total distance and then you divide by two and get 11 miles. You are technically supposed to do it with the equation, but that is just a shortcut I use and it works every time.
distance between eachother (4); sum of distances (26)
and you divide by 2 because it was the sum of two people's distances... if it were 3 people you would divide by 3... 4 people you would divide by 4... and so on...
well ok thanks
so there are 2 methods to solve this equation... 1. simultaneously where the equations are s = steve and K = kevin s + k = 26 k - s = 4 the alternative is let steve = s miles kevin = s + 4 so use the sum s + s + 4 = 26 then 2s + 4 = 26 and solve for s either method gives the correct answer

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