In January of 2013 Greg wrote to tell us that this answer is incorrect. See his message below.

Hi Robert,

If you knew the selling price it would be straightforward to check to see if it gives $100000.00\$$ net. You would take off 6% of the selling price (selling price × 0.06) for the commission, 6% of the selling price for the federal tax and 7.5% of the selling price for the provincial tax. If you had the correct selling price you would be left with 100000.00$.

Let me write that out again but rather than use the term "selling price" just use the letter S to stand for the selling price.

Start with the selling price.

S

Take off 6% of S.

S - 0.06 × S

Take off another 6% of S

S - 0.06 × S - 0.06 × S

Take off an additional 7.5% of S

S - 0.06 × S - 0.06 × S - 0.075 × S

The result must be 100000.00

S - 0.06 × S - 0.06 × S - 0.075 × S = 100000.00

0.06 + 0.06 + 0.075 = 0.195 so the equation becomes

S - 0.195 × S = 100000.00

1 - 0.195 = 0.805 so

0.805 × S = 100000.00

or

S = 100000.00/0.805 = 124223.60$

Penny

Commission applies to the final sale price NO TAX on sale.
But both taxes 6% and 7.5% apply ONLY to the 6% commission of the sale price.
Greg

Thanks for this greg.

Again let S be the selling price in dollars. The commission is 6% of the selling price so the commission is $0.06 \times S.$ The tax of $6\% + 7.5\% = 13.5\%$ applies only to the commission so the tax is $0.135 \times 0.06 \times S.$ When the commission and tax are subtracted from seling price the result must be $100,000\$$ and thus

\[S - 0.06 \times S - 0.135 \times 0.06 \times S = 100,000\]

When I solved this for S I got S = $107,307.65\$$

Penny