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Math Help - Word Problems!

  1. #1
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    Question Word Problems!

    A. A board is 20 feet long. It is going to be cut into three pieces. The longest piece is 4 times as long as the shortest. The middle piece is 2 feet longer then the shortest piece. How long is each piece?

    Alright so this is what I have so far.
    A = Unknown
    B = A+2
    C = A*4

    A+B+C=20

    I have figured most numbers that might work.. but I am guessing it is a decimal number, and I would rather not guess and get it right.. I want to understand how this problem might work. x.x I was wondering if someone might help me with that?
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    B. There are two barrels of salt solution. The first barrel is a 20% solution. The second barrel is a 40% solution.
    I: The Second barrel has 42 gallons. How much salt is in the barrel?
    II: You add the contents of the first barrel to the second barrel. The resulting solution has a concentration of 35%. How many gallons were there in the first Barrel?

    This one.. I have no clue where to even start.. I am assuming you eventually would have to make the 20/40% into decimals but aside from that, it is up in the air..
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    C. You are buying a $220,000 home and must place a 20% down payment. How much is the down payment.

    Answer: I made 20% into .2 decimal form and simply multiplied it into $220,000 getting a solution of $44,000?
    20% is 1/5 of 100% so to check this I took (44,000 x 4) and got the base. I am pretty confident this one is right.
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    D. Your friend tells you she went to a sale that gave her 30% off. She says that she saved $50. How much was her total purchase?

    I want to approach this one like I did the last one..? Is there any information you can give me concerning it. I figure I will have to turn the 30% into .3 decimal but I am not sure what to do with it then. );
    Last edited by Uriah5356; March 11th 2009 at 11:04 PM.
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  2. #2
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    Since the longest and middle pieces are explained in terms of the shortest piece, lets call the shortest piece x.

    Since the longest is 4 times the shortest, then the longest = 4x.
    Since the middle is 2 feet longer, the the middle = x+ 2.

    Now since all pieces add up to 20...make an equation.

    4x + (x + 2) + x = 20
    6x = 18
    x = 3.

    Now plug in x and you'll have all the lengths.
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  3. #3
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    Quote Originally Posted by jzellt View Post
    Since the longest and middle pieces are explained in terms of the shortest piece, lets call the shortest piece x.

    Since the longest is 4 times the shortest, then the longest = 4x.
    Since the middle is 2 feet longer, the the middle = x+ 2.

    Now since all pieces add up to 20...make an equation.

    4x + (x + 2) + x = 20
    6x = 18
    x = 3.

    Now plug in x and you'll have all the lengths.
    Oooh! O.O Thank you! x-x Strange thought I checked three, shows where my mind is.
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  4. #4
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    Problem A:

    a+b+c = 20
    b = a+2
    c = 4a

    This means that a+b+c = 20 = a+a+2+4a = 6a+2
    6a+2 = 20
    6a = 18
    a = 3
    b = a+2 = 5
    c = 4a = 12

    Problem B:

    I'm sorry, doing this one would take 20 minutes, and typing it here would take another 10. (if it's done the way I think it is)

    Problem C:

    Answer: I made 20% into .2 decimal form and simply multiplied it into $220,000 getting a solution of $44,000?
    20% is 1/5 of 100% so to check this I took (44,000 x 4) and got the base. I am pretty confident this one is right.
    Correct if in the last sentence - to check this I took (44,000 x 4) - you meant 5 instead of four. Just to make sure: answer is indeed 44.

    Problem D:

    You know the old price was a 100% and the new price is 70% (30% of)

    You know that 30% = 50.

    You can do this several ways, for instance divide 70 by 30 and multiply by 50. Or you take the 50$ (30%) and divide by three = 16,666$ (10%) and then multiply by 7 = 166,67$ (70%)
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