SOLUTION: I've been trying to help my daughter, but it's been too long since I've done any algebra. She is currently in graphs, but this does not seem to fit. Anyway, here is the question

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Question 570735: I've been trying to help my daughter, but it's been too long since I've done any algebra. She is currently in graphs, but this does not seem to fit. Anyway, here is the question posed.
A rectangular hole 2cm wide and x cm long is cut in a rectangular sheet of metal 7/2cm wide and y cm long. The length of the hole is 1 cm less than the length of the metal sheet. After the hole is cut, the area of the remaining metal is 11cm squared. Find the length of the hole and the length of the metal sheet.
I'm math stupid and having a difficult time trying to find help.
Thank you for any suggestions,
Jeff R.
Found 2 solutions by scott8148, mananth:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"The length of the hole is 1 cm less than the length of the metal sheet" ___ x + 1 = y

"After the hole is cut, the area of the remaining metal is 11cm squared" ___ (2*x) + 11 = (7/2)*y

substituting ___ 2x + 11 = (7/2)(x + 1) ___ 2x + 11 = (7/2)x + (7/2) ___ 4x + 22 = 7x + 7

solve for x, then substitute back to find y

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
It is obvious that we have to find the length & width of the hole and the sheet.
the length of hole =x which is 1cm less than the length of the sheet
x=y-1
Area = L*W
width of hole =2cm
Length of hole = x cm
highlight%28Area+of+hole+=+2x%29
-----
width of sheet = 7/2 cm
length of sheet = y
highlight%28area+of+sheet+=+%287y%2F2%29+cm%5E2%29
Area of sheet - area of hole = balance area =11cm^2


%287y%2F2%29+-+2x+=+11
substitute x in this equation
%287y%2F2%29-2%28y-1%29=11%29
multiply the equation by 2 to eliminate the denominator
7y-4(y-1)=22
7y-4y+4=22
3y=18
/3
]y=6 cm
length of sheet = 6 cm
length of hole is 1 less than length of sheet
so length of hole = 6-1 =5 cm

CHECK
area of sheet - area of hole = 11
7/2 * 6 - 5*2=11
11=11