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Thread: Find the number of pencils and the number of pens that Sharon can buy if she has to b

  1. #1

    Find the number of pencils and the number of pens that Sharon can buy if she has to b

    A wooden pencil costs 30 cents and a pen costs 55 cents. Sharon is given $9.50 and is told to spend the money as much as possible on at least one pencil and at least one pen. However, for every pen that she buys, she must buy at least 3 pencils. Find the number of pencils and the number of pens that Sharon can buy if she has to buy the greatest possible number of items.
    Last edited by mmm4444bot; 02-03-2018 at 04:26 AM. Reason: matched author edit on duplicate post, then deleted duplicate post

  2. #2
    Elite Member
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    Quote Originally Posted by sheejave View Post
    A wooden pencil costs 30 cents and a pen costs 50 cents. Sharon is given $9.50 and is told to spend the money as much as possible on at least one pencil and at least one pen. However for every pen that she buys, she must buy at least 3 pencils. Find the number of pencils and number of pens that Sharon can buy if she has to buy the greatest possible number of items.
    What are your thoughts?

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  3. #3
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    Quote Originally Posted by sheejave View Post
    A wooden pencil costs 30 cents and a pen costs 55 cents. Sharon is given $9.50 and is told to spend the money as much as possible on at least one pecil and at least one pen. However, for every pen that she buys, she must buy at least 3 3 pencils. Find the number of pencils and the number of pens that Sharon can buy if she has to buy the greatest possible number of items.
    Is this the same problem as you had posted before:
    https://www.freemathhelp.com/forum/t...costs-50-cents
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  4. #4
    55 X no. of pens + 30 X no.of pencils <= 950

    I am not sure how to proceed next.

    Thanks in advance

  5. #5
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by sheejave View Post
    55 X no. of pens + 30 X no.of pencils <= 950

    I am not sure how to proceed next.
    Try following the hint provided earlier: "What happens if Sharon buys only 1 pen?"

    What is your response?

  6. #6
    Quote Originally Posted by stapel View Post
    Try following the hint provided earlier: "What happens if Sharon buys only 1 pen?"

    What is your response?
    .55 + .3x <= 9.5

    x <= 29.8

  7. #7
    Quote Originally Posted by sheejave View Post
    .55 + .3x <= 9.5

    x <= 29.8
    0.55 * 2 + 0.3 * x <= 9.5
    x = 28

    To find the solution of this problem, do you use the trial and error method or is there an algebraic way?

  8. #8
    Quote Originally Posted by Denis View Post
    Btw, 1st post shows .50 for pens, 2nd shows .55
    I am sorry, it's 55 cents

  9. #9
    Quote Originally Posted by Denis View Post
    Then your x =< 29.8 is correct.
    Needs to be rounded down to 29.
    1 @ .55 = .55
    29 @ .30 = 8.70
    .55 + 8.70 = 9.25
    9.50 - 9.25 = .25 not spent

    The book shows the answer as 2 pens and 28 pencils (you need to spend as much money as possible and buy the greatest possible number of items).

    Is there any algebraic method to solve this?

    Thanks

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