how many envelopes can be made out of a sheet of paper 3m 24cm by 1m 72cm,if each envelope requires a piece of paper of side 18cm by 12cm?
the sheet of paper is
324 cm by 172 cm
The tempation is to say:
area of whole paper = 55728 cm^2
area of 1 envelope = 216
so we have 55728/216 or 258 envelopes.
BUT, not so fast .....
If we lay the length of the envelope along the long side of the large sheet, we can get 324/18 or 18 along that side
the number of envelopes along the short side is 172/12 = 14 1/3
but we need whole numbers,
so number of envelopes = 18x14 or 252
with some waste of paper.
If we lay the width of the envelope along the long side of the large sheet, we can get 324/12 or 27 of them, but then along the other side we would get 172/18 or 9.55..
Again we could only get 9 rows, for a number of envelopes of 27x9 = 243
The largest number of envelopes is 252
To find out how many envelopes can be made out of a given sheet of paper, we need to determine how many times the smaller envelope size can fit within the larger sheet of paper.
First, let's convert the measurements of the sheet of paper and the envelope into a consistent unit, let's say centimeters.
The dimensions of the sheet of paper are 3m 24cm by 1m 72cm.
Converting meters to centimeters:
3m = 3 * 100cm = 300cm
1m = 1 * 100cm = 100cm
Therefore, the dimensions of the sheet of paper are 300cm by 172cm.
The dimensions of the envelope are 18cm by 12cm.
To find out how many envelopes can fit in the larger sheet of paper, we need to divide the length and width of the paper by the length and width of the envelope, respectively.
For the length:
Number of envelopes = Length of the paper / Length of the envelope
Number of envelopes = 300cm / 18cm
For the width:
Number of envelopes = Width of the paper / Width of the envelope
Number of envelopes = 172cm / 12cm
Calculating the number of envelopes:
Number of envelopes = (300cm / 18cm) * (172cm / 12cm)
Simplifying the equation:
Number of envelopes = (300 * 172) / (18 * 12)
Now, let's calculate the value:
Number of envelopes = 51600 / 216
Number of envelopes = 239
Therefore, you can make 239 envelopes out of the given sheet of paper.