Algebra 2 Problems! Help!?

Hi. I'm in Algebra 2, and I'm doing my homework and I can't figure out how to do these two problems. I understand everything else besides these two. Can you help me understand these so that I can fully understand what I'm learning and so that later on I can pass my test. Thanks.

Here's the problems:

1. Suppose you want to put a frame around the painting with the dimensions 24"x16". The frame will be the same width around the entire painting. You have 276in.^2 (squared) of framing material. How wide should the frame be? What does 276in.^2 represent in this situation? How can you write the dimensions of the frame using two binomials?

2. Suppose you have an outdoor pool measuring 25ft. by 10ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft. thick and you have 304ft.^3 (cubed) of cement, how wide should the walkway be?

Please help me understand how to do both of these problems. I would really appreciate it. Thank you.

Comments

  • The frame width = x

    It will add x on both ends of the width and height so the entire frame + picture will have dimensions

    (2x + 24)(2x + 16) = 4x^2 + 80x + 384 by FOIL

    The picture itself has area 16 x 24 = 384 so you subtract that from the total to get the frame in terms of x

    Frame area = 4x^2 + 80x and you know that is 276

    4x^2 + 80x = 276

    4x^2 + 80x - 276 = 0 divide by 4

    x^2 + 20x - 69 = 0 Factor

    (x + 23)(x - 3) = 0

    so x = -23 (impossible) or x = 3

    On the other, you find the area of the walkway:

    Volume = l•w•t

    304 = l • w • 1

    so l • w = 304÷1 = 304 = area of walkway

    Then from there it's just like above

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