Calculate the total price of a merchandise with added tax

Discussion in 'Middle School / Junior High' started by NoviceTutor, Apr 13, 2015.

  1. NoviceTutor

    NoviceTutor Companion

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    Apr 13, 2015

    Hello,

    The solved math word problem goes like this, "A new computer costs $600 plus 7% sales tax. How much is the cost of the computer with added tax?"

    Solution given: The total cost of the computer with added tax = 600 x 1.07 = 642.

    I am used to solve this type of problem using a different method which involves two steps: First calculate the amount of sales tax. Second, add the tax amount to the price of the computer.

    Where does the 1 in the number 1.07 come from? :unsure:

    Your explanation will be greatly appreciated.
     
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  3. vickilyn

    vickilyn Multitudinous

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    Apr 14, 2015

    I use this all the time! The 1 is the cost of the computer before the tax. If the sales tax is 7%, you could make this a two part calculation by stating that the cost of the computer is $600

    The amount of tax on the computer is $600 x 7%. We would write that as $600 x .07. The answer to that calculation is $42.

    We would them have to add the tax of $42 to the cost of the computer, $600, to find the total cost of computer with tax, $642.

    However, you can cut a step by multiplying by 1.07, which inserts the cost of the computer into the calculation when you multiply times 1, and then add all of the products.

    You can do multiple steps, but this is especially handy if you are using a simple calculator and want to cut out the additional steps. It also prevents you from giving an answer that only considers the sales tax, so a handy way to do the calculation. Hope that helps.
     
  4. TeacherGroupie

    TeacherGroupie Moderator

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    Apr 14, 2015

    .07 is a way to express 7%, the tax rate, yes? By the same token, 1 is 100%: the whole of the base cost of the computer. The distributive property - which states that ac + ad = a(c + d) - tells us that, other things being equal, it doesn't much matter whether we state this problem as 600(100%) + 600(7%) or as 600(100% + 7%). But most of us can add 100 + 7 in our heads, whereas calculating the tax from the percentage and then adding that back to the base cost takes a little longer, so adding the percentages before multiplying by the base price of the computer is a legitimate option.
     
  5. vickilyn

    vickilyn Multitudinous

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    Apr 14, 2015

    Teacher Groupie's answer is more instructive to you, by far. I am not the "teacher teacher" that she is - but I was honest - doing this calculation is one way I use math in everyday life all the time. It is a good example of math in action, a skill set that students tend to remember.
     
  6. Upsadaisy

    Upsadaisy Moderator

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    Apr 14, 2015

    The one is the 100% of the price; ie, the original cost. So it is automatically added to the tax.
     
  7. NoviceTutor

    NoviceTutor Companion

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    Apr 14, 2015

    Thank you everyone for the wonderful explanations. I truly see what is going on now.
     
  8. a2z

    a2z Virtuoso

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    Apr 14, 2015

    Can you extrapolate the concept to sale items with tax?

    A computer cost 1000 and is 30% off in a state that has 5% sales tax. What is the total cost of the computer assuming you don't buy the extended warranty?
     
  9. horned_Frog89

    horned_Frog89 Companion

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    Apr 14, 2015

    This math concept is VERY valuable. In my current job, I am a sales tax consultant, so I am using the *1.%% trick EVERY DAY.

    I also find taxable amounts, tax rates and other figures given a combination of amounts or rates.

    a2z: In your example, I would multiply 1000*.7 to get a sales price of $700.

    Then, $700*1.05 to get a final price of 735.
     
  10. prealgebra-nerd

    prealgebra-nerd Rookie

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    May 8, 2015

    The 1 is the original cost of the item, the .07 is the additional tax :)
     

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