Price calculation where the service fee and the sales tax both increase with the other

[agust]

I'm stuck with a price calculation where the service fee and the sales tax both increase with the other, if you catch my drift.

I sell an item for which I want to earn 100$ after sales tax and service fee. The sales tax is 10% and the service fee is 5%. How do I calculate the price? What do I multiply or divide 100 with to reach the correct price?

For example, if I do: 100 * (1 + 0.10 + 0.05) = 115, I will then lose 5.75 in service fee and 11.50 in sales tax, leaving me with 97.75. And If I try: (100 * 1.10) * 0.05 = 115.50, I then lose 5.78 in service fee and 11.55 in sales tax, leaving me with 98.17.

I've tried to figure it out, but I seem to lack the math skills necessary... Very thankful for help!

 

[stapel]

I'm stuck with a price calculation where the service fee and the sales tax both increase with the other, if you catch my drift.

Are you saying that their amounts each rely on the other's amount somehow?

I sell an item for which I want to earn 100$ after sales tax and service fee. The sales tax is 10% and the service fee is 5%. How do I calculate the price?

The taxes are ten percent of *what*, exactly? The fee is five percent of *what*, exactly? (If they are ten and five percent, respectively, of the price, then their values do not actually rely on each other, but are based solely on the selling price.)

What do I multiply or divide 100 with to reach the correct price?

I'm sorry, but I don't know what you mean by the above?

For example, if I do: 100 * (1 + 0.10 + 0.05) = 115, I will then lose 5.75 in service fee and 11.50 in sales tax, leaving me with 97.75. And If I try: (100 * 1.10) * 0.05 = 115.50, I then lose 5.78 in service fee and 11.55 in sales tax, leaving me with 98.17.

I've tried to figure it out, but I seem to lack the math skills necessary...

Unfortunately, any hints or helps we might provide won't likely make much sense until you learn the background material (which was supposed to have been covered in class first, before assigning homework on it). Fortunately, there are loads of lessons available online. [listing]

Please study at least two lessons in the listing, and then attempt the exercise. If you get stuck, you can then reply with a clear listing of your efforts so far, at which point we can begin to work with you, starting with finding ten and five percent of the selling price [imath]s[/imath].

(this) is (some percent) of (that)

...where "is" means "equals" and "of" means "times".

 

[lev888]

I'm stuck with a price calculation where the service fee and the sales tax both increase with the other, if you catch my drift.

I sell an item for which I want to earn 100$ after sales tax and service fee. The sales tax is 10% and the service fee is 5%. How do I calculate the price? What do I multiply or divide 100 with to reach the correct price?

For example, if I do: 100 * (1 + 0.10 + 0.05) = 115, I will then lose 5.75 in service fee and 11.50 in sales tax, leaving me with 97.75. And If I try: (100 * 1.10) * 0.05 = 115.50, I then lose 5.78 in service fee and 11.55 in sales tax, leaving me with 98.17.

I've tried to figure it out, but I seem to lack the math skills necessary... Very thankful for help!

Is this a class assignment or a 'real life' question? Doesn't really matter though, since the answer is "It depends on the rules for the application of the fees". So ask the teacher or the authority responsible for the taxes and fees whether they both apply to the base price or one as applied after the other.

 

[Steven G]

I'm stuck with a price calculation where the service fee and the sales tax both increase with the other, if you catch my drift.

I sell an item for which I want to earn 100$ after sales tax and service fee. The sales tax is 10% and the service fee is 5%. How do I calculate the price? What do I multiply or divide 100 with to reach the correct price?

For example, if I do: 100 * (1 + 0.10 + 0.05) = 115, I will then lose 5.75 in service fee and 11.50 in sales tax, leaving me with 97.75. And If I try: (100 * 1.10) * 0.05 = 115.50, I then lose 5.78 in service fee and 11.55 in sales tax, leaving me with 98.17.

I've tried to figure it out, but I seem to lack the math skills necessary... Very thankful for help!

After arriving at 115, how are you computing that you lose 5.75 in service fee and 11.50 in sales tax?
(100 * 1.10) is a bit more than 100--it is exactly 110. How do you take a small percent, like 5% = 0.05 of 110 and get more than 110, like 115.50?
(100*1.10)*0.05 = (110)*0.05 = 5.5 NOT 115.50.


You want to make 100. So after buying the item, paying sales tax and service fee you ADD $100 to that amount in order to make $100 profit. Is that now clear.

Example. If you purchase an item for $100, then with sales tax and fees you will pay $100*(1 + .10 + .05) = $100(1.15) = $115. This is your total cost to purchase this item. You want to profit $100, then when you sell this item you need to get in your left hand $115 (your total cost) and in your right hand you need to get $100 (your profit). That is you need to collect $115 + $100 = $215


In general, if the item you purchase is $x, the the total cost to you will be $x(1+.10+.05) = $x(1.15). Now add on your profit of $100. You should charge $x(1.15) + $100.

 

[agust]

Thank you for helping out!

Are you saying that their amounts each rely on the other's amount somehow?

Yes, perhaps... Let me try to be more clear below.

The taxes are ten percent of *what*, exactly? The fee is five percent of *what*, exactly? (If they are ten and five percent, respectively, of the price, then their values do not actually rely on each other, but are based solely on the selling price.)

The "what" here is the selling price. I need to figure out how to calculate the selling price when I only know the amount I want to end up with (after taxes and fees).

If the selling price is e.g. 115$, and the service fee is calculated on the selling price of 115 and the sales tax is also calculated on the selling price of 115, I will end up with 115 - 11,5 - 5,75 = 97,75$. If I need to end up with 100$, how do I calculate what selling price to charge?

 

[agust]

Is this a class assignment or a 'real life' question? Doesn't really matter though, since the answer is "It depends on the rules for the application of the fees". So ask the teacher or the authority responsible for the taxes and fees whether they both apply to the base price or one as applied after the other.

Thanks for reaching out. It's real life. The fees are applied as follows:

10% sales tax on selling price (total amount I bill)
5% service fee on selling price (total amount I bill)

 

[agust]

Appreciate your help!

After arriving at 115, how are you computing that you lose 5.75 in service fee and 11.50 in sales tax?

Because the sales tax and service fee are both (and separately) calculated on the selling price (total amount I bill). 0.1 * 115 = 11.5. 0.05 * 115 = 5.75. I can not calculate the service fee on the amount excl. tax.

You want to make 100. So after buying the item, paying sales tax and service fee you ADD $100 to that amount in order to make $100 profit. Is that now clear.

100$ is not the profit I seek. 100$ is what I need to end up with after having paid taxes and fees.

 

[lev888]

Thank you for helping out!



Yes, perhaps... Let me try to be more clear below.



The "what" here is the selling price. I need to figure out how to calculate the selling price when I only know the amount I want to end up with (after taxes and fees).

If the selling price is e.g. 115$, and the service fee is calculated on the selling price of 115 and the sales tax is also calculated on the selling price of 115, I will end up with 115 - 11,5 - 5,75 = 97,75$. If I need to end up with 100$, how do I calculate what selling price to charge?

The price is x. What is the expression for 10% of x? And 5%? Subtract them from x. Set the result equal to 100. Solve for x.