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Math Help - Please Need Help Fast World Problems

  1. #1
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    Arrow Please Need Help Fast World Problems

    I am suppose to list variables and give equations. I have six word problems in my homework that I can not seem to figure out I know that of at least 3 that have to use the supply and demand model and another one has to do with mixtures plus motion. I would truly appreciate the help Check them out below:

    1. A company budgets $30,000 for advertisement costs promoting a new product. Television ads cost $500 each and radio ads cost $100 each. If the company wants to buy a total of 220 ads, how many of each kind of ads should the company buy?

    2. A charity sells tickets for a fundraising dinner. Each adult's ticket costs $10 and each child's ticket costs $5. A total of $1050 was raised by selling 130 tickets. How many of each kind of ticket was sold?

    3. A chemist needs 110 milliters of a 31% solution but has only 10% and 43% solutions available. How many milliters of each should be mixed to get the desired solution?

    4. The weekly demand model for a new toy is given by D=-5p+80. The weekly supply model for the same toy is 5=3p+40. For these models, p is the price of the toy and N is the number of toys sold or supplied each week to the toy store. Find the price at which supply and demand are equal.

    5. A college student earned $8200 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 8% and the rest at 7%. If the student received a total of $613 in interest at the end of the year. How much was invested at 8%?

    6. A twin-engined aircraft can fly 816 mi. from city A to city B in 3 hrs. with the wind and make the return trip in 8 hrs. against the wind. What is the speed of the wind?


    I have been trying all night to figure out these word problems Please help
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  2. #2
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    Quote Originally Posted by MathIlliterate View Post
    I am suppose to list variables and give equations. I have six word problems in my homework that I can not seem to figure out I know that of at least 3 that have to use the supply and demand model and another one has to do with mixtures plus motion. I would truly appreciate the help Check them out below:

    1. A company budgets $30,000 for advertisement costs promoting a new product. Television ads cost $500 each and radio ads cost $100 each. If the company wants to buy a total of 220 ads, how many of each kind of ads should the company buy?
    Let the number of a TV add be t, and of radio add be r.

    30000 = 500.t + 100.r,

    or dividing through by 100:

    300 = 5.t + r.

    But the total number of adds is to be 220, so:

    220 = t + r.

    So you now have a pair of simultaneous linear equations to solve.

    Subtract the second from the first to get:

    300 - 220 = (5.t + r) - (t + r),

    simplify:

    80 = 4.t,

    or t=20, so r=200.

    RonL
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  3. #3
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    Thank You

    Thanks for your help on that word problem sorry about the double post Anymore help would be greatly appreciated.
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  4. #4
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    Quote Originally Posted by MathIlliterate View Post
    I am suppose to list variables and give equations. ...

    5. A college student earned $8200 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 8% and the rest at 7%. If the student received a total of $613 in interest at the end of the year. How much was invested at 8%?

    ...
    Hello,

    let x be the money invested at 8%
    let y be the money invested at 7%

    Then you get a pair of simultaneously equations:
    x + y = 8200
    0.08*x + 0.07*y = 613

    For confirmation only: x = 3900; y = 4300

    EB
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    You Rock earboth!

    Thanks for your help I am truly appreciative
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  6. #6
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    Quote Originally Posted by MathIlliterate View Post
    I am suppose to list variables and give equations. ...

    6. A twin-engined aircraft can fly 816 mi. from city A to city B in 3 hrs. with the wind and make the return trip in 8 hrs. against the wind. What is the speed of the wind?[/B]

    ...
    Hello,

    the general formula to use is:
    \text{way}=\text{speed} \cdot \text{time}

    Let be v_a=\text{speed of airplane} and v_w=\text{speed of wind}

    You get a pair of two simultaneously equations:
    816=(v_a+v_w) \cdot 3
    816=(v_a-v_w) \cdot 8

    Expand the RHS and rearrange. Solve for v_a and v_w

    For confirmation only: v_a = 187 mph; v_w = 85 mph

    EB
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  7. #7
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    Quote Originally Posted by MathIlliterate View Post
    I am suppose to list variables and give equations. ...


    3. A chemist needs 110 milliters of a 31% solution but has only 10% and 43% solutions available. How many milliters of each should be mixed to get the desired solution?
    ...
    Hello,

    let x be the amount of the 10%-solution and
    let y be the amount of the 43%-solution.

    Then you get a pair of simultaneously equations:

    x + y = 110
    0.1*x + 0.43*y = 0.31*110

    for confirmation only: x = 40; y = 70

    EB
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  8. #8
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    Quote Originally Posted by MathIlliterate View Post
    I am suppose to list variables and give equations. ...


    2. A charity sells tickets for a fundraising dinner. Each adult's ticket costs $10 and each child's ticket costs $5. A total of $1050 was raised by selling 130 tickets. How many of each kind of ticket was sold?

    ...
    Hello,

    let a be the number of adult's tickets and
    let c be the number of child's tickets.

    Then you get a pair of simultaneously equations:

    a + c = 130
    10*a + 5*c = 1030

    For confirmation only: a = 76; c = 54

    EB
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  9. #9
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    Thank You

    Your the bomb earboth! I understand the break down of each word problem now. Thanks
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