Question

Please answer fast: Tanya owns a small business. She must add 8% sales tax to the initial cost of the job. She then adds 15% to the cost, including sales tax, to find the amount to charge a client. Tanya charges one client a total of $465.75 for a job. Calculate the initial cost of this job.

Answer 1

Given:

Sales tax to be added to the initial cost = $8$%

Tax added to the initial cost for a client = $15$%

Amount charged by Tanya for a job = $$465.75$

To find:

To calculate the initial cost of the job.

Formula to be used:

• Let the initial cost of the job be denoted by "$x$".
• It is given that some percentage of amount is charged as tax which includes the sales tax also.
• Let the total amount charged be denoted by "$T$" and the percentage of sales tax be denoted by "$P$".
• Now, the total cost of the job is calculated as follows:

$T=(P/100)x+x\\T=((P/100)+1)x$......(1)

Using the above equation, the initial cost "$x$" can be calculated by substituting the given "$T$" value.

Solution:

• As per the given data, $15$% of the tax is added to the initial cost to get total cost for a job and the tax includes sales tax also, which is mandatory.
• Using the given data and the equation (1), the initial cost of the job is calculated as follows:

$T=((P/100)+1)x\\465.75=((15/100)+1)x\\465.75=(0.15+1)x\\465.75=1.15x\\x=465.75/1.15\\x=405$

⇒The initial cost of the job = $$405$

Final Answer:

∴The initial cost charged by Tanya for the job is $$405$.