Tutoring math, you revisit this type of problem often.  The math tutor gives a quick reminder just ahead of exams.

Here’s the problem:

A saleswoman gets paid a base monthly salary plus commission.  One month she sells $50 000 and gets paid a total of $4200.  Another month she sells $75 000 and gets a total of $5700.  Find her base salary and commission rate.

Like any word problem, we begin with let statements:

let x=base salary
let y=commission rate

We set up the equations that reflect the two months’ earnings:

x+50000y=4200
x+75000y=5700

In a situation like this, substitution is easy. Looking at the first equation above, we notice that if x+50000y=4200, then x=4200 – 50000y. We can then substitute 4200 – 50000y for x in the other equation:

(4200 – 50000y) + 75000y = 5700

Continuing, we simplify the left side:

4200 – 50000y + 75000y=5700

4200+25000y=5700

Now we subtract 4200 from both sides:

25000y=1500

Finally we divide both sides by 25000:

y=1500/25000=0.06

Substitute the known value of y into either equation to find x:

x+50000(0.06)=4200

Simplify:

x+3000=4200

Subtract 3000 from both sides:

x=1200

To answer the problem: the saleswoman’s base monthly salary is $1200, while her commission rate is 0.06. Note, of course, that 0.06 is the same as 6 percent.

Hope your exam prep is going well:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.