Quick questions on Commission, piecework, royalties and government payments for HSC Maths Standard 2

A flat-rate commission is the simplest case: one rate on the whole amount sold. Multiply the sales by the rate as a decimal. Some jobs pay a retainer as well, a guaranteed base amount the worker keeps even if they sell nothing, with the commission added on top. The bar below builds a week's pay for a car salesperson on a $480 retainer plus $3\%$ commission, who sells $92000 of cars.

A sliding scale pays different rates on different bands of the sale price. Real estate commission is the classic case: a higher rate on the first slice of the price, then lower rates on the larger amounts. The crucial idea is that this is a marginal structure, exactly like a tax scale. Each rate applies only to the part of the sale inside its band, not to the whole sale.

Piecework pays a fixed amount for each unit of work completed, so the pay is just the rate per unit multiplied by the number of units. A garment machinist paid $4.25 per finished item who completes $168$ items earns $168 \times 4.25 = 714$, i.e. $714.00. The hours taken are irrelevant; only the count of items is paid.

A royalty is a percentage of the revenue (or sometimes the profit) from intellectual property, paid to its creator. Intellectual property means something a person created, such as a book, song or invention. The arithmetic is identical to a flat commission, but the percentage is taken on the money the work earns. Take an author on a $10\%$ royalty whose book sells $3200$ copies at $32.95.

Some people receive a pension, allowance or benefit from the government. These are almost always quoted per fortnight, because that is how the government pays them. The Year 11 maths is converting between periods, exactly as for a salary: multiply a fortnightly amount by $26$ to get a yearly figure, or read the correct row from a table of rates. An allowance of $562.80 per fortnight is $562.80 \times 26 = 14632.80$, i.e.