Commission (HSC SSCE Mathematics Standard): Revision Notes

Worked Example: Basic Commission Calculation

Question: Zoë sold a house for $650,000. Find the commission from the sale if her rate of commission was $1.25\%$.

Solution:

We need to find the commission earned.

Convert the percentage to a decimal and multiply by the sale price:

$\text{Commission} = 1.25\% \text{ of } \$650,000$

$= 0.0125 \times 650,000$

$= \$8,125$

Answer: Zoë earned $8,125 in commission from this sale.

Exam tip: Always remember to convert the percentage to a decimal before multiplying. To do this, divide the percentage by 100 (or move the decimal point two places to the left).

Worked Example: Base Salary Plus Commission

Question: An electrical goods salesman is paid $570.50 per week plus $4\%$ commission on all sales over $5,000 per week. Find his earnings in a week where his sales amounted to $6,800.

Solution:

First, calculate the sales amount that qualifies for commission. Since commission is only paid on sales over $5,000:

$\text{Sales qualifying for commission} = 6,800 - 5,000$

$= 1,800$

Now calculate the total earnings by adding the base weekly payment and the commission:

$\text{Earnings} = \text{Base pay} + \text{Commission}$

$= 570.50 + (4\% \text{ of } \$1,800)$

$= 570.50 + (0.04 \times 1,800)$

$= 570.50 + 72$

$= \$642.50$

Answer: The salesman's earnings for that week were $642.50.

Exam tip: When commission only applies to sales above a threshold, always subtract the threshold amount first before calculating the commission percentage.