Hally A.
asked • 11/27/15find the length and width of the envelope
the length of a rectangular envelope is 2 1/2 times its width. A plastic band surrounds the front and back of the envelope to secure it. the plastic band is 39 3/8 inches long. find the length and width of the envelope.
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1 Expert Answer
Don L. answered • 11/28/15
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Fifteen years teaching and tutoring basic math skills and algebra
Hi Hally, let x represent the width of the envelop. Then the length is 2 and 1 / 2 times x. If the band going around the envelop is 39 and 3 / 8 inches, we can find the width of the envelop.
We will discount any thickness in the envelop. That means one half of the band covers the front of the envelop and one half covers the back.
Find one half of band:
Change the mixed fraction 39 and 3/8 to an improper fraction.
((39 * 8) + 3) / 8 = 315 / 8
Divide by 2:
(315 / 8) / 2 = 315 / 16 = 19 and 11 / 16
The width of the envelop is 19 and 11 / 16 inches.
The length is 2 and 1 /2 times the width.
5 / 2 * 315 / 16 = 1575 / 32 = 49 and 7 / 32
The length of the envelop is 49 and 7 / 32 inches.
Questions?
Inactive Tutor
Alternate solution: If band is parallel to the longest dimension "L".
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11/28/15
Don L.
tutor
Hi Norbert, good point. If the band was parallel to the length, then the length of the envelop would be 19 and 11 / 19 inches in length.
Since the length is 2 and 1 / 2 times the width, the width would be 7 and 7 / 8 inches.
Questions?
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11/28/15
Frankellys S.
If the band that goes around the envelope is 39 3/8 inches how is the length(49 7/32) Of the envelope going to be more than band that goes around the envelope?
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02/28/16
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11/27/15