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Math Help - help in word problems, urgent!

  1. #1
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    help in word problems, urgent!

    the ones that i have MAJOR problems on are 2, 4, and 6. the rest i can probably do myself.

    PLEASE, i do not know who to start any of these problems.

    2.
    An investment firm has $100,000 to invest for a client and decides to invest it int two stocks A and B. The expected annual rate of return, or interest, for stock A is 15%, but there is some risk involved, and the client does not wish to invest more than $50,000 in this stock. the annual rate of return on the more stable stock B is anticipated to be 10%. Determine how much should be invested at each rate so that the annual interest from these investments is 12,000.

    3.
    A chemist has 10 ml of a solution that contains a 30% concentration of acid. How many pure acid must be added in order to increase the concentration to 50%?

    4.
    A radiator contains 8 quarts of a mixture of water and antifreeze. If 40% of the mixture is antifreeze, how much of the mixture should be drained and replaced by pure antifreeze so that resultant mixture will contain 60% antifreeze?

    5.
    Two cities are connected by means of a highway. A car leaves city A at 1:00 PM and travels at a constant rate of 40 mi/h toward city B. 30 minutes later, another car leaves A and travels towards B at a constant rate of 55 m/h. At what time will be second car overtake the first car?

    6.
    A pharmacist is to prepare 15 ml of special eye drops for a glaucoma patient. The eye drop solution must have a 2% active ingredient, but the pharmacist only has 10% solution and 1% solution in stock. How much of each type of solution should be used to fill the prescription?

    7.
    It takes a boy 45 mins to deliver the newspapers on his route; however if his sister helps, it takes them only 20 minutes. How long would it take his sister to deliver the newspapers by herself?
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  2. #2
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    nr. 4 only

    Quote Originally Posted by jaden View Post
    the ones that i have MAJOR problems on are 2, 4, and 6. the rest i can probably do myself....
    4.
    A radiator contains 8 quarts of a mixture of water and antifreeze. If 40% of the mixture is antifreeze, how much of the mixture should be drained and replaced by pure antifreeze so that resultant mixture will contain 60% antifreeze?
    ...
    Hello, jaden,

    I'll do problem nr. 4 step by step:

    1. contents of pure antifreeze: 0.4 * 8 = 3.2
    2. amount of mixture to be drained: x
    3. therefore missing antifreeze: 0.4 * x
    4. amount of added pure antifreeze: x

    Now you can put together all parts to an equation:
    \frac{0.4 * 8 - 0.4*x+x}{8}=0.6

    Solve for x. I've got x = \frac{8}{3}
    (Remark: Please check my calculations. I'm the king of mistakes here)

    EB
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  3. #3
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    nr. 6 only

    Quote Originally Posted by jaden View Post
    the ones that i have MAJOR problems on are 2, 4, and 6. the rest i can probably do myself.
    PLEASE, i do not know who to start any of these problems.
    ...
    6.
    A pharmacist is to prepare 15 ml of special eye drops for a glaucoma patient. The eye drop solution must have a 2% active ingredient, but the pharmacist only has 10% solution and 1% solution in stock. How much of each type of solution should be used to fill the prescription?
    ...
    Hello, jaden,

    I'm going to "translate" your problem into a system of equations:

    1. amount of 10%-solution: x
    2. amount of 1%-solution. 15-x

    Now you get an equation which describes the problem:

    10%*x+1%*(15-x) = 2%*15. I'm going to use fractions:
    \frac{1}{10}x+\frac{1}{100}(15-x)=\frac{2}{100} \cdot 15

    Solve for x. I've got: x=\frac{5}{3}

    Therefore the pharmacist use \frac{5}{3} ml of the 10%-solution and \frac{40}{3} ml of the 1%-solution to get 15 ml of a 2%-solution.

    EB
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  4. #4
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    prob nr. 2 finally

    Quote Originally Posted by jaden View Post
    the ones that i have MAJOR problems on are 2, 4, and 6. the rest i can probably do myself.

    PLEASE, i do not know who to start any of these problems.

    2.
    An investment firm has $100,000 to invest for a client and decides to invest it int two stocks A and B. The expected annual rate of return, or interest, for stock A is 15%, but there is some risk involved, and the client does not wish to invest more than $50,000 in this stock. the annual rate of return on the more stable stock B is anticipated to be 10%. Determine how much should be invested at each rate so that the annual interest from these investments is 12,000.
    ...
    Hello, jaden

    this problem is similar to the two I answered already. So I'll give you all details to start and leave the final calculations for you.
    If you need further information then say so, please.

    1. invested sum in stock A: x
    2. invested sum in stock B: 100.000 - x
    3. 15 % = 0.15 and 10% = 0.1

    0.15x + 0.10*(100.000 - x) = 12.000

    Now solve this equation for x and afterwards you can calculate y too.

    EB
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  5. #5
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    thanks so much for your first two posts.

    for the investment problem, i got 40,000 dollars for stock a and 60,000 dollars for stock b
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  6. #6
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    Quote Originally Posted by jaden View Post
    thanks so much for your first two posts.

    for the investment problem, i got 40,000 dollars for stock a and 60,000 dollars for stock b
    Hello, jaden,

    that's what I got too. Congratulations!

    EB
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