Total pay for the year (x) = Base pay + (percentage commission)*x, where x is the number of karaoke machines sold.
Total pay (x) = $35,470 + ($1,300/machine) * (1.145)*x = $38,486. The 1.145 factor represents the unit price of each machine sold PLUS the 14.5% commission.
Let's begin solving this for x by subtracting $35,470 from both sides of this equation. The result is $3,016, which represents commission income.
Each machine sells for $1,300, and the saleswoman earns 14.5% on each sold. That comes to 1.145($1,300) = $1488.50 per machine sold.
Dividing both sides of this equation by ($1,488.50/machine), we get
$3016
x = ------------------------- = 2.027. Round this off to 2, representing the
$1488.50 commission earned on the sale of
2 machines.
