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Thread: I need a formula to this problem: solve x = 20000, y = 15% of z, y + z = x for y, z

  1. #1
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    Question I need a formula to this problem: solve x = 20000, y = 15% of z, y + z = x for y, z

    Hi, this is my first post. I need a formula to the following problem:

    x = 20000
    y = 15% of z
    y + z = x

    How do you solve for y and z? What is the formula to the solution?

    With x being 20000 I know that roughly y = 2608.7 and z = 17391.3, but that was just from me guessing and then adjusting a few dozen times. I need to know the actual formula to solve for y and z.

    And this has a practical purpose if anyone is interested. We own a small business and we have a certain budget for marketing. That budget needs to include commission to the marketing company and what is left will go to the actual ad spend. The commission is 15% of the ad budget. So as our budget goes up or down I need to be able to calculate what the commission and ad spend will be without going over our overall budget. I can continue to guess and adjust but there must be a more practical formula to do that.

    Thanks,

    -Mort

  2. #2
    Quote Originally Posted by Mort View Post
    Hi, this is my first post. I need a formula to the following problem:

    x = 20000
    y = 15% of z
    y + z = x

    How do you solve for y and z? What is the formula to the solution?

    With x being 20000 I know that roughly y = 2608.7 and z = 17391.3, but that was just from me guessing and then adjusting a few dozen times. I need to know the actual formula to solve for y and z.

    And this has a practical purpose if anyone is interested. We own a small business and we have a certain budget for marketing. That budget needs to include commission to the marketing company and what is left will go to the actual ad spend. The commission is 15% of the ad budget. So as our budget goes up or down I need to be able to calculate what the commission and ad spend will be without going over our overall budget. I can continue to guess and adjust but there must be a more practical formula to do that.

    Thanks,

    -Mort
    Since x=20000 and y + z = x, then y + z = 20000.
    Since y = 15% of z, then y = 0.15z

    Combining those two statements gives 0.15z + z = 20000, that is 1.15*z = 20000.

    Dividing both sides by 1.15 gives z = 17391.30

    Now y = 15% of z = 15% of 17391.30 = 2608.70 (rounded)

    Hope that helps.
    Heavens to Murgatroyd!!

  3. #3
    Quote Originally Posted by Harry_the_cat View Post
    Since x=20000 and y + z = x, then y + z = 20000.
    Since y = 15% of z, then y = 0.15z

    Combining those two statements gives 0.15z + z = 20000, that is 1.15*z = 20000.

    Dividing both sides by 1.15 gives z = 17391.30

    Now y = 15% of z = 15% of 17391.30 = 2608.70 (rounded)

    Hope that helps.
    This is absolutely right.

  4. #4
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    Quote Originally Posted by Harry_the_cat View Post
    Since x=20000 and y + z = x, then y + z = 20000.
    Since y = 15% of z, then y = 0.15z

    Combining those two statements gives 0.15z + z = 20000, that is 1.15*z = 20000.

    Dividing both sides by 1.15 gives z = 17391.30

    Now y = 15% of z = 15% of 17391.30 = 2608.70 (rounded)

    Hope that helps.
    Thank you so much! My brain was really hurting when I was trying to figure this out. I'll be plugging this into an excel sheet to help us make the calculations. Thanks again!

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