Question 209737: A rectangular hole 3 cm wide and x cm long is cut in a rectangular sheet of metal that is 4 cm 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 sheet is 20 cm squared. Find the length of the hole(x) and the length of the metal sheet (y).
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular hole 3 cm wide and x cm long is cut in a rectangular sheet of
metal that is 4 cm 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 sheet is 20 cm squared.
Find the length of the hole(x) and the length of the metal sheet (y).
:
Hole area = 3x
Sheet metal area 4y
:
Metal area - hole area = 20 sq/cm
4y - 3x = 20
:
It also says,
"The length of the hole is 1 cm less than the length of the metal sheet."
therefore
y - x = 1
y = (x + 1)
:
Substitute for y in the area equation, find x
4(x+1) - 3x = 20
4x + 4 - 3x = 20
4x - 3x = 20 - 4
x = 16 cm; length of the hole
and
y = 16 + 1
y = 17 cm is the length of the metal
;
:
Check solution in the area equation
4(17) - 3(16) =
68 - 48 = 20
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