Re: Precalculus Question

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Posted by Mary on October 01, 2002 at 21:20:20:

In Reply to: Re: Precalculus Question posted by Brad Paul on September 29, 2002 at 12:28:48:

: : : : Hi,

: : : : I'm can't figure out how to approach this question"

: : : : Suppose we want to make a poster containing 50 square inches of printed matter surrounded by a 3" border at the top and bottom, and a 2" border along each side. How does the total area of the poster depend on the width of the printed matter?.

: : : : Any clues, anyone? Please?

: : : Let A be the area of the printed matter, and w the width of the
: : : printed matter. If the printed matter is in the shape of a rectangle
: : : we can find the height of the printed matter via h=A/w. Let b be the
: : : 3 inch border at the top and bottom and c be the 2 inch width of the
: : : border along each side. Now with these variable lets write an equation
: : : for the total area of the poster. Lets call it A_total

: : :
: : : A_total=(2 c+w)(2 b+A/w)

: : : Notice this equation is just a height time width equation. The width
: : : is 2 time the border width because there is one on each side and the
: : : the width of the printed matter. The height is 2 times the borders
: : : plus height written in terms of the Area and width of the printed
: : : matter.

: : It wouldn't be:
: : A = (6+w)(4+w) and therefore A = 24 + w(10+w) since we know the printed matter is a square and the complete poster is a rectangle? Also, how would i show this as a function of w? Would it be expressed as A(w) = 24 + w(10+w) since i need to show how the total area is dependent on the width of the printed material.....Thanks!

: I did not take from the question that the printed area is a
: square. The question says:

: "a poster containing 50 square inches of printed matter"

: The words "square inches" is a measure of area not a statement of
: geometry. One can say that a circle has the area of 100 square
: inches. This is why I express the height of the printed area as
: h=A/w. Where A=50 inch².

: Be sure to clearly distinguish between the area of the printed area (my
: A) and the total area of the poster (my A_total)

Thank you. That makes sense.

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: : : : : Hi, : : : : : I'm can't figure out how to approach this question" : : : : : Suppose we want to make a poster containing 50 square inches of printed matter surrounded by a 3" border at the top and bottom, and a 2" border along each side. How does the total area of the poster depend on the width of the printed matter?. : : : : : Any clues, anyone? Please? : : : : Let A be the area of the printed matter, and w the width of the : : : : printed matter. If the printed matter is in the shape of a rectangle : : : : we can find the height of the printed matter via h=A/w. Let b be the : : : : 3 inch border at the top and bottom and c be the 2 inch width of the : : : : border along each side. Now with these variable lets write an equation : : : : for the total area of the poster. Lets call it Atotal : : : : : : : : Atotal=(2 c+w)(2 b+A/w) : : : : Notice this equation is just a height time width equation. The width : : : : is 2 time the border width because there is one on each side and the : : : : the width of the printed matter. The height is 2 times the borders : : : : plus height written in terms of the Area and width of the printed : : : : matter. : : : It wouldn't be: : : : A = (6+w)(4+w) and therefore A = 24 + w(10+w) since we know the printed matter is a square and the complete poster is a rectangle? Also, how would i show this as a function of w? Would it be expressed as A(w) = 24 + w(10+w) since i need to show how the total area is dependent on the width of the printed material.....Thanks! : : I did not take from the question that the printed area is a : : square. The question says: : : "a poster containing 50 square inches of printed matter" : : The words "square inches" is a measure of area not a statement of : : geometry. One can say that a circle has the area of 100 square : : inches. This is why I express the height of the printed area as : : h=A/w. Where A=50 inch2. : : Be sure to clearly distinguish between the area of the printed area (my : : A) and the total area of the poster (my Atotal) : Thank you. That makes sense.

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