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Math Help - Two word problems.

  1. #1
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    Two word problems.

    First:

    A company purchases a billboard on the side of the highway for $10,000. For each person that calls the number on the billboard and fills out an application, the company receives $100. 15% of people who call the number actually fill out an application. What is the minimum number of calls that need to be made so that the company can make a profit off the billboard?

    Second:

    A company sends out an email to 1,000,000 people to register for an event. The email has a 8% open rate, 5% click-through rate, 200 registrations at $10/registration. What is the cost per click?

    I had a hard time with these two at a recent interview.

    Thanks in advance.
    Last edited by mr fantastic; June 30th 2011 at 01:29 PM. Reason: Title.
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  2. #2
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    Re: Help me solve two word problems ...

    For the first one,

    Let x be the amount of people filling out an application

    Let y be the total amount of people calling

    Solve the system:

    100x = 10000

    0.15y = x

    What do you get?
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  3. #3
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    Re: Help me solve two word problems ...

    x = 100
    y = 667 people

    Correct?
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  4. #4
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    Re: Help me solve two word problems ...

    I'm pretty sure.

    But why don't you check it yourself?

    I.e. is 100 equal to 15% of 667?
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  5. #5
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    Re: Two word problems.

    Hello, llckll!

    A company purchases a billboard on the side of the highway for $10,000.
    For each person that calls the number on the billboard and fills out an application,
    the company receives $100.
    15% of people who call the number actually fill out an application.

    What is the minimum number of calls that need to be made
    so that the company can make a profit off the billboard?

    \text{Let }x\text{ = number of calls made.}

    \text{15\% of them will fill out an application.}
    . . 0.15x\text{ applications are filled.}

    \text{Each application earns \$100.}
    . . \text{The company gets: }\:100(0.15x) \,=\,15x\text{ dollars}

    \text{This amount must be at least \$10,000.}
    . . 15x\:\ge \:10,\!000 \quad\Rightarrow\quad x \:\ge\:666\tfrac{2}{3}


    \text{Therefore, there must be at least 667 calls.}

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  6. #6
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    Re: Two word problems.

    WHY are about 99% of problems called "word problems"?!
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  7. #7
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    Re: Two word problems.

    Do you have a confidence interval for that proportion Wilmer?

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  8. #8
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    Re: Two word problems.

    Quote Originally Posted by pickslides View Post
    Do you have a confidence interval for that proportion Wilmer?
    That sounds like a "word problem"!
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