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Math Help - a few word problems

  1. #1
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    a few word problems

    1) An open box with length x feet,width y feet, and height 2 feet is shown below. It is known that the surface area for this box is 92 square feet and the equation to xy+4x+4y=92. Express the volume of this box as a function of x.

    2) Two children were bouncing a ball. During one particular bounce, the ball traveled a horizontal distance of 6 feet and its maximum height above the ground was 4 feet. The path was in the shape of a parabala. Find the standard equation of the parabala described by this information. Let x replresent the horizontal distance in feet from the point the bounce started and y represent the height about the ground in feet.

    3) IN math club, 1 team sold 2 different types of shirts. T shirts sold for 9 dollars a piece while sweatshirst sold for 16 dollars a piece. The secretary misplaced the individualized order forms but knows 57 total people placed an order and has written a check in the amound of 751 dollars to cover the entire order. If x represents the number of t shirts ordered and y the number of sweatshirts ordereed, choose the system of equations that can be used to find x and y. Do not solve.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    1) An open box with length x feet,width y feet, and height 2 feet is shown below. It is known that the surface area for this box is 92 square feet and the equation to xy+4x+4y=92. Express the volume of this box as a function of x.
    okay, you are given with xy+4x+4y=92.
    now, V = lwh = 2xy.. we want a function of x, so we need y in terms of x.. from the equation of the surface area, we have
    xy+4y=92-4x \implies y(x+4) = 92 - 4x \implies y = \frac{92 - 4x}{x+4}

    therefore, V = 2x \left( {\frac{92 - 4x}{x+4}} \right)

    Quote Originally Posted by vc15ao4 View Post
    2) Two children were bouncing a ball. During one particular bounce, the ball traveled a horizontal distance of 6 feet and its maximum height above the ground was 4 feet. The path was in the shape of a parabala. Find the standard equation of the parabala described by this information. Let x replresent the horizontal distance in feet from the point the bounce started and y represent the height about the ground in feet. .
    this is more on application (physics) and pardon me, im not good at this topic..

    Quote Originally Posted by vc15ao4 View Post
    3) IN math club, 1 team sold 2 different types of shirts. T shirts sold for 9 dollars a piece while sweatshirst sold for 16 dollars a piece. The secretary misplaced the individualized order forms but knows 57 total people placed an order and has written a check in the amound of 751 dollars to cover the entire order. If x represents the number of t shirts ordered and y the number of sweatshirts ordereed, choose the system of equations that can be used to find x and y. Do not solve.
    this is the system:

     {\begin{array}{ccc}<br />
x+y & = & 57 \\<br />
9x + 16y & = & 751 \\<br />
\end{array}}
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