legionspawn187
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- Apr 28, 2011
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You are going to make a box out of cardboard. The box needs to measure 10cm by 5cm by 5cm; 10% of the final product will be wasted in the cutting process. How much cardboard do I need?
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- Thread starter legionspawn187
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Hello, legionspawn187!
\(\displaystyle \text{There are four panels which are }10 \times 5.\)
. . \(\displaystyle \text{Their area is: }\:4 \times (10\cdot5) \:=\:200 \text{ cm}^2\)
\(\displaystyle \text{There are two panels which are }5 \times 5.\)
. . \(\displaystyle \text{Their area is: }\:2 \times (5\cdot5) \:=\:50 \text{ cm}^2\)
\(\displaystyle \text{The box will require: }\:200 + 50 \:=\:250\text{ cm}^2\text{ of cardboard.}\)
\(\displaystyle \text{This is 90\% of the total cardboard needed.}\)
. . \(\displaystyle 0.90C \:=\:250 \quad\Rightarrow\quad C \:=\:\frac{250}{0.9} \:=\:\frac{2500}{9}\)
\(\displaystyle \text{Therefore, you will need }277\tfrac{7}{9}\text{ cm}^2\text{ of cardboard.}\)
\(\displaystyle \text{There are four panels which are }10 \times 5.\)
. . \(\displaystyle \text{Their area is: }\:4 \times (10\cdot5) \:=\:200 \text{ cm}^2\)
\(\displaystyle \text{There are two panels which are }5 \times 5.\)
. . \(\displaystyle \text{Their area is: }\:2 \times (5\cdot5) \:=\:50 \text{ cm}^2\)
\(\displaystyle \text{The box will require: }\:200 + 50 \:=\:250\text{ cm}^2\text{ of cardboard.}\)
\(\displaystyle \text{This is 90\% of the total cardboard needed.}\)
. . \(\displaystyle 0.90C \:=\:250 \quad\Rightarrow\quad C \:=\:\frac{250}{0.9} \:=\:\frac{2500}{9}\)
\(\displaystyle \text{Therefore, you will need }277\tfrac{7}{9}\text{ cm}^2\text{ of cardboard.}\)
legionspawn187 said:
You never stated whether it is an open box or a closed box.
You did not specify what/how this cutting process will be
as it is done to the piece of cardboard.
You did not state what shape the piece of cardboard is, such as
rectangular, square, etc.
Get these stated and then the solvng of the problem may proceed.