Question 202442
Let 

x = length of shorter pipe

y = length of longer pipe


Since "One length of hot water pipe is 3 feet longer than the other", this means that {{{y=x+3}}}


Also, since "their combined length is 27 feet", we get {{{x+y=27}}}




{{{x+y=27}}} Start with the second equation.



{{{x+x+3=27}}} Plug in {{{y=x+3}}}.



{{{2x+3=27}}} Combine like terms on the left side.



{{{2x=27-3}}} Subtract {{{3}}} from both sides.



{{{2x=24}}} Combine like terms on the right side.



{{{x=(24)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=12}}} Reduce.



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Since we know that {{{x=12}}}, we can use this to find {{{y}}}.



{{{x+y=27}}} Go back to the second equation.



{{{12+y=27}}} Plug in {{{x=12}}}.



{{{y=27-12}}} Subtract {{{12}}} from both sides.



{{{y=15}}} Combine like terms on the right side.



So the solutions are {{{x=12}}} and {{{y=15}}}.



This means that the shorter pipe is 12 feet long while the longer pipe is 15 feet long.