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%.