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Math Help - Help Me Please

  1. #1
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    Help Me Please

    Use the 5-step method to solve.

    1. Jim has a total of 50 coins. Some are nickels and some are dimes. Altogether he has $4.15. How many dimes and nickels does he have?

    2. A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.

    3. When the digits of a two-digit number are reversed the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?

    4. Erin's age is 3 times Waren's. In 4 years she will be twice as old as he will be. how old is each now?

    Please help me in figuring out these answers. I'm not so sure in how to solve them. Thanks.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by poeticprincess View Post
    1. Jim has a total of 50 coins. Some are nickels and some are dimes. Altogether he has $4.15. How many dimes and nickels does he have?
    Let the number of nickels be n and the number of dimes be d.

    Then
    n + d = 50
    0.05*n + 0.10*d = 4.15

    Solving the top equation for d:
    d = 50 - n

    Insert this into the bottom equation:
    0.05*n + 0.10*[50 - n] = 4.15

    0.05*n + 5.00 - 0.10*n = 4.15

    -0.05*n = 4.15 - 5.00 = -0.85

    n = (-0.85)/(-0.05) = 17

    Thus d = 50 - 17 = 33

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by poeticprincess View Post
    2. A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.
    Let the +x direction be the direction of the current. Let the distance the sailboat travels downstream be d = 20 miles. Let the speed of the boat in still water be v (with respect to the water.) Let the speed of the water be w (with respect to the ground.)

    So the speed of the boat downstream with respect to the ground is v + w. So it covers the distance d in a time t given by:
    d = (v + w)t --> t = 3 hours

    When the boat moves upstream its speed with respect to the ground will be v - w. So it covers the distance d in a time T given by:
    d = (v - w)T --> T = 4 hours


    Thus
    20 = 3(v + w) = 3v + 3w
    20 = 4(v - w) = 4v - 4w

    Solve the top equation for w:
    w = (1/3)(20 - 3v) = (20/3) - v

    Insert this into the bottom equation:
    20 = 4v - 4[(20/3) - v]

    20 = 4v - (80/3) + 4v

    8v = 20 + (80/3) = 140/3

    v = 140/24 = 35/6 mph

    So w = (20/3) - 35/6 = 5/6 mph

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by poeticprincess View Post
    3. When the digits of a two-digit number are reversed the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?
    Call the number xy, that is to say 10*x + y. If we reverse the number we get yx, that is to say 10*y + x and we know that yx = xy + 9 or
    (10*y + x) = (10*x + y) + 9

    And
    x + y = 9

    Solve this equation for y:
    y = 9 - x

    Insert this into the first equation:
    10*[9 - x] + x = 10*x + [9 - x] + 9

    90 - 10x + x = 10x + 9 - x + 9

    90 - 9x = 9x + 18

    18x = 72

    x = 72/18 = 4

    Thus y = 9 - 4 = 5

    So the number is 45.

    -Dan
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by poeticprincess View Post
    4. Erin's age is 3 times Waren's. In 4 years she will be twice as old as he will be. how old is each now?
    Let Erin's age be x and Waren's age be y. Then
    x = 3y
    x + 4 = 2(y + 4)

    So inserting the top equation into the bottom:
    3y + 4 = 2(y + 4)

    3y + 4 = 2y + 8

    y = 4

    So x = 3*4 = 12.

    -Dan
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  6. #6
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    Thnx a lot topsquark!
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