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Math Help - Solving equations, a couple questions!

  1. #1
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    Solving equations, a couple questions!

    I have these questions on my homework but I have no idea how the answer is how it is. Thank you for answering!

    1. Solve this equation for C.
    S=C+rC
    I know that the answer is S/1+r= c
    I do not know where the 1 comes from.


    2. You have 36.75$ to spend on a sweathshirt. There is a 5% sales tax. What is the most the sweatshirt can cost?
    How do you solve this?

    3. Solve this equation for B1:
    A=1/2h (b1 + b2)

    The answer is 2a/h -b1
    Whenever I do it, I get 2a-b1/h
    I do not know what I am doing wrong.


    4. A garden is 46 feet wide and 84 feet long. The garden has a path around it that is 10 feet wide. The cost of fencing is 9$ per foot. How much will it cost to put a fence around the path?

    Here, I do not get how to draw a picture or get the equation.


    Thank you so much to anyone who takes the time to answer all of my questions! I have a midyear on monday and I really need to know these answers for it.
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  2. #2
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    Quote Originally Posted by cherrybaby View Post
    I have these questions on my homework but I have no idea how the answer is how it is. Thank you for answering!

    1. Solve this equation for C.
    S=C+rC
    I know that the answer is S/1+r= c
    I do not know where the 1 comes from.
    S = C +rC

    S = C(1 + r)

    (We factored out the C)

    Divide by (1 + r)

    Thus, S/(1 + r) = C
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  3. #3
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    Quote Originally Posted by cherrybaby View Post

    2. You have 36.75$ to spend on a sweathshirt. There is a 5% sales tax. What is the most the sweatshirt can cost?
    How do you solve this?

    3. Solve this equation for B1:
    A=1/2h (b1 + b2)
    2. You want the sweatshirt to cost, at most, x + .05x <= $36.75

    Solve for x;

    1.05x = 36.75

    x = 35

    Thus, you want the sweatshirt to cost, AT MOST, $35.

    Check:

    $35*(.05) = $1.75 (this is the sales tax)

    $35 + $1.75 = $36.75;

    If the sweatshirt is any more, the sales tax would be greater and thus would exceed this amount.

    3. A = (1/2)*h*(b_1 + b_2)

    Multiply by 2;

    2A = h*(b_1 + b_2)

    Divide by h;

    2A/h = b_1 + b_2

    2A/h - b_1 = b_2
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  4. #4
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    Quote Originally Posted by cherrybaby View Post
    4. A garden is 46 feet wide and 84 feet long. The garden has a path around it that is 10 feet wide. The cost of fencing is 9$ per foot. How much will it cost to put a fence around the path?

    Here, I do not get how to draw a picture or get the equation.
    Soroban, I am sure, will be able to draw you a nice picture. I am not sure how to, unfortunately. Any way;

    The garden alone is 84 x 46;

    But, since we have a path around it that is 10 feet wide, we have to include 5 feet on each side;

    Thus, it's 89 feet long by 51 feet wide;

    The question is asking for the perimeter;

    2W + 2L = P

    2(51) + 2(89) = 280 feet of fencing

    But, we have that it is $9 per foot; thus,

    280*9 = $2520
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  5. #5
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    Thank You so much for responding aftershock! My only problem is with the last problem, where I know that the answer is 3060, and I do not know how to get that answer. (I was supplied with an answer key, but it does me know me good.)
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  6. #6
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    Quote Originally Posted by cherrybaby View Post
    Thank You so much for responding aftershock! My only problem is with the last problem, where I know that the answer is 3060, and I do not know how to get that answer. (I was supplied with an answer key, but it does me know me good.)
    Stupid question if you ask me; two ways of interpreting it. They are interpreting it as follows:

    The garden alone is 84 x 46;

    Now, the path is 10 feet wide all around; thus, 10 at the top and 10 at the bottom, and 10 on each of the sides...

    So 104, 104, 66, 66;

    P = 2(104) + 2(66)

    = 340

    340*9 = $3060
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