Jason, a hard working BCIT student, has a summer job at McTaggart Plywood where he is paid by commission based on his sales of lumber and plywood products. In June, he was paid $4950, for his lumber sales of $30,000 and plywood sales of $42,000. In July, he was paid $4620, for his lumber sales of $51,500 and plywood sales of $20,400.

What commission rate is he paid for each product?

Solution:

Let L = Commission rate Jason is paid for lumber sales.

Let P = Commission rate Jason is paid for plywood sales.

In general,

Jason’s monthly commission = (Jason’s lumber sales for the month)*L + (Jason’s plywood sales for the month)*P

Therefore,

[June] $4950 = $30,000 * L + $42,000 * P

[July] $4620 = $51,500 * L + $20,400 * P

We have two equations in two unknowns, L and P, which we may solve using many different algebraic techniques. Lets use Cramer’s Rule.

Therefore the commission rate Jason is paid for lumber is 6.0% and for plywood is 7.5%.