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

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SUMMARY

This discussion focuses on calculating the individual portions of two tax rates (6% and 6.5%) from a known total tax amount. The user seeks a formula to determine how much of the total tax due corresponds to each rate when given the total tax amount. The solution involves using the total sale amount (T) to derive the individual tax amounts through the equations 0.125T = Total Tax Due and subsequently calculating each portion using the respective tax rates. For example, with a total tax of $150, the calculations yield $72 for the 6% portion and $78 for the 6.5% portion.

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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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