Question 351952
Let x = length of larger piece and y = length of smaller piece



Since "a piece of fabric 180 inches long", this means that {{{x+y=180}}}



Also, because the fabric "cut into two pieces such that 3 times the larer piece exceeds 4 times the smaler piece by 85 inches", this means that {{{3x=4y+85}}}



{{{x+y=180}}} Start with the first equation.



{{{y=180-x}}} Subtract x from both sides.



{{{3x=4y+85}}} Move onto the second equation



{{{3x=4(180-x)+85}}} Plug in {{{y=180-x}}}



{{{3x=720-4x+85}}} Distribute.



{{{3x=-4x+805}}} Combine like terms on the right side.



{{{3x+4x=805}}} Add {{{4x}}} to both sides.



{{{7x=805}}} Combine like terms on the left side.



{{{x=(805)/(7)}}} Divide both sides by {{{7}}} to isolate {{{x}}}.



{{{x=115}}} Reduce.



{{{y=180-x}}} Go back to the previously isolated equation.



{{{y=180-115}}} Plug in {{{x=115}}}



{{{y=65}}} Subtract



So the solutions are {{{x=115}}} and {{{y=65}}} which means that the larger piece is 115 inches and the smaller piece is 65 inches long.



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Jim