Here’s the problem:<\/p>\n
A saleswoman gets paid a base monthly salary plus commission. \u00a0One month she sells $50 000 and gets paid a total of $4200. \u00a0Another month she sells $75 000 and gets a total of $5700. \u00a0Find her base salary and commission rate.<\/p>\n
Like any word problem, we begin with let statements:<\/p>\n
let x=base salary
\nlet y=commission rate<\/p>\n
We set up the equations that reflect the two months’ earnings:<\/p>\n
x+50000y=4200
\nx+75000y=5700<\/p>\n
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:<\/p>\n
(4200 – 50000y) + 75000y = 5700<\/p>\n
Continuing, we simplify the left side:<\/p>\n
4200 – 50000y + 75000y=5700<\/p>\n
4200+25000y=5700<\/p>\n
Now we subtract 4200 from both sides:<\/p>\n
25000y=1500<\/p>\n
Finally we divide both sides by 25000:<\/p>\n
y=1500\/25000=0.06<\/p>\n
Substitute the known value of y into either equation to find x:<\/p>\n
x+50000(0.06)=4200<\/p>\n
Simplify:<\/p>\n
x+3000=4200<\/p>\n
Subtract 3000 from both sides:<\/p>\n
x=1200<\/p>\n
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.<\/p>\n
Hope your exam prep is going well:)<\/p>\n