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Math Help - Story Problems

  1. #1
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    Story Problems

    Please and Thank you

    Jim and Joe started on trips from San Francisco and traveled in opposite directions. Jim traveled 15 km/h faster than Joe. After 4 hours, they were 420 km apart. How fast was each person traveling?

    A coin bank contains more than $3 in quarters, dimes, and nickels. The # of dimes is twice the # of quarters and the # of nickels is 3 times the # of quarters. Find the least possible # of quarters in the bank.

    Cynthia invested 3 times as much money at 6% as at %5. If the total of simple interest is at least $1150, what is the least possible amount Cynthia has invested at 5%?

    Michael drove to a friend's house at a rate of 40 m/h. He came back by the same route, but at a rate of 45 m/h. If the roundtrip took less than 4 hrs, what is the greatest possible distance Michael could have traveled to visit his friend?

    Caridad is6 years older than her sister. For years ago she was 4 times as old as her sister. How old is Caridad now?

    Jims average score on 3 tests is 82. What is the least he can score on his 4th test so his average will be at least 86?
    Last edited by peachgal; September 22nd 2008 at 07:37 PM.
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  2. #2
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    Quote Originally Posted by peachgal View Post
    Please and Thank you

    Jim and Joe started on trips from San Francisco and traveled in opposite directions. Jim traveled 15 km/h faster than Joe. After 4 hours, they were 420 km apart. How fast was each person traveling?

    Let Joe's speed = x km/h
    so, Jim's speed = (x+15) km/h

    Distance travelled by Joe in 4 hours= speed . time = 4x

    Distance travelled by Jim in 4 hours= 4(x + 15)

    Total distance = 420

    4x + 4(x + 15) = 420

    Now solve it.
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  3. #3
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    Quote Originally Posted by peachgal View Post
    Please and Thank you

    A coin bank contains more than $3 in quarters, dimes, and nickels. The # of dimes is twice the # of quarters and the # of nickels is 3 times the # of quarters. Find the least possible # of quarters in the bank.
    Let # dimes = d
    # nickels = n
    # quarters = q

    d = 2q
    and n = 3q

    Total money,

    0.25q + 0.10d + 0.05n > 3

    0.25q + 0.10 (2q) + 0.05 (3q) > 3

    Now solve.
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  4. #4
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    Quote Originally Posted by peachgal View Post
    Please and Thank you

    Cynthia invested 3 times as much money at 6% as at %5. If the total of simple interest is at least $1150, what is the least possible amount Cynthia has invested at 5%?
    Let money invested at 5% = $ x
    So, money invested at 6% = $ 3x

    simple interest =

    0.05x + 0.06 (3x) \ge 1150

    now solve.
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  5. #5
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    Quote Originally Posted by peachgal View Post
    Please and Thank you

    Michael drove to a friend's house at a rate of 40 m/h. He came back by the same route, but at a rate of 45 m/h. If the roundtrip took less than 4 hrs, what is the greatest possible distance Michael could have traveled to visit his friend?
    Let distance to his friend's house = x metres.

    Time taken to go = \frac{\text{Distance}}{\text{speed}}=\frac{x}{40}

    Time taken to come back = \frac{\text{Distance}}{\text{speed}}=\frac{x}{45}

    Total time < 4 h

    \frac{x}{40} + \frac{x}{45} <4

    Now, finish up.
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  6. #6
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    Quote Originally Posted by peachgal View Post
    Please and Thank you
    Caridad is 6 years older than her sister. For years ago she was 4 times as old as her sister. How old is Caridad now?
    Her sister's age = x yrs.

    Caridad's age = (x + 6) yrs.

    Four years ago,

    Her siter's age = x - 4

    Caridad's age = x + 6 - 4 = x + 2

    Now,

    x + 2 = 4 (x - 4)

    Now, finish up. did you get it???
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  7. #7
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    Quote Originally Posted by peachgal View Post
    Please and Thank you
    Jims average score on 3 tests is 82. What is the least he can score on his 4th test so his average will be at least 86?
    Total score of first 3 tests = 3 \times 82 = 246

    Total score of all 4 tests = 4 \times 86 = 344

    score on the 4th test = 344 - 246 = 98

    Did you get it?????
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