Finding fixed known %'s of total when total % known

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Discussion Overview

The discussion revolves around determining the portions of two different tax rates (6% and 6.5%) from a known total tax amount due, given the total sale amount. Participants explore the mathematical relationships involved in calculating these portions based on the total tax due.

Discussion Character

  • Mathematical reasoning
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks to find a formula to calculate the portions of tax based on a total tax amount and total sale amount.
  • Another participant states that if the individual tax rates are known, the calculation is straightforward, but if they are not known, it is impossible to determine the portions.
  • A participant provides a mathematical breakdown showing how to derive the total sale amount from the total tax due and subsequently calculate the portions for each tax rate.
  • Further clarification is provided through an example that illustrates the calculation process using percentages.

Areas of Agreement / Disagreement

Participants generally agree that knowing the individual tax rates simplifies the calculation process. However, there is no consensus on how to approach the problem when only the total tax due is known without additional information.

Contextual Notes

Some participants express confusion about the calculations and seek further clarification, indicating that the problem may involve assumptions about the relationship between the total tax and the sale amount.

vitamin1
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Hi,

I am trying to figure out the equation of the following so that I can make a formula in a spread sheet.

There are two tax rates... 6.5% and 6% equaling 100% of total tax due for a sale (sale amounts vary).

If I am only given the TOTAL (100%) tax due, in this case \$125, how can I work backwards and know what portion of the \$125 is 6% and what portion is 6.5%?

i.e.
  • \$1000 = total sale
  • 6% = 60
  • 6.5% = 65
  • 100% of total tax due = \$125
  • I am only given total sale and total tax due. How can I work backwards from the two known and get \$60 and \$65?

Hope that makes sense! Thanks.
 
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Hi vitamin and welcome to MHB! :D

If you know the individual tax rates that are applied, it's straightforward (you did it yourself above). If you don't know the individual tax rates that were applied it's impossible.

By the way, preceding dollar signs with a '\' allows your post to render correctly - dollar signs have a special meaning here - they are used for typesetting math (latex).
 
greg1313 said:
Hi vitamin and welcome to MHB! :D

If you know the individual tax rates that are applied, it's straightforward (you did it yourself above). If you don't know the individual tax rates that were applied it's impossible.

By the way, preceding dollar signs with a '\' allows your post to render correctly - dollar signs have a special meaning here - they are used for typesetting math (latex).

Thanks for the dollar sign tip.

I guess I'm just not getting it.

Tell me how you figure the following out equation wise:

Total tax is \$150.
What portion is 6% and what portion is 6.5% ?
 
Let $T$ be the total sale amount (the amount of the sale before taxes).

$$0.125T=150\implies T=1200$$

$$0.06\times1200=72$$

$$0.065\times1200=78$$

Does that help?
 
greg1313 said:
Let $T$ be the total sale amount (the amount of the sale before taxes).

$$0.125T=150\implies T=1200$$

$$0.06\times1200=72$$

$$0.065\times1200=78$$

Does that help?

That did help...thanks!

I also saw another example that helped as follows:

12.5% = 150
so
6% = 150 / 12.5 * 6 = 72
6.5% = 150 / 12.5 * 6.5 = 78
 

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