How Do I Calculate Tax and Service Costs from a Total Price in Algebra?

[Iguanahump]

I'm 58 and I'm afraid my math skills are not what they used to be. I have been working on this problem for days now and have the correct answer, but only by trial and error. I'm working on a spreadsheet that will calculate a discount off a base price. All I have is the total price, which includes a service cost of .006 of the base price + a 15% tax on the service cost. In order to do this I need to know the base price. Since the total price includes the 15% tax, I need to be able to calculate the tax amount, deduct it and then calculate the service cost. How do I calculate the tax before I know the base price or the service cost? This is the best as I can represent it in a formula:

x = 998,500 - (.15y)
y = x/1.006

Any assistance would be appreciated.

 

[Anhar Miah]

Hello, as far as I can't understand your question:

you have the total cost, let us call this Tc, this Tc is made up from a base price, let us call this B, and also a Service cost, let us call this S, and a Tax on the service cost let us call this Tx, thus:

$$T_{c} = B+S+T_{x}$$

and $$T_{x} = 0.15B$$

and $$S = B-0.006$$ thus:

$$T_{c} = B + (B-0.006) + (0.15B)$$

and I assume you wish to calculate the base price?

 

[Iguanahump]

Thank you for your assistance. The way you diagrammed it is correct, with the exception that Tx = .15S. I need to know B, that way I can calculate S and Tx easily.

 

[tiny-tim]

Welcome to PF!

Hi Iguanahump! Welcome to PF!

If I've understood it right:

S = 0.006B;

tax = 0.15S = 0.15 0.006B = 0.0009B;

so total = B + S + tax = B(1 + 0.15 + 0.0009) = 1.1509B.