Q: Steve Trinter, an electronics salesman, earns a weekly salary plus a commission on sales. One week he sold $4000 in merchandise and was paid $660. The next week his sales totaled $6000, and his pay was $740. Find his weekly salary and his commission rate.
A: I am going to define our variables:
X = percent of commission (as a decimal) and let
Y = his weekly salary
So, we can use the information from the problem to set up these two equations:
Week 1: 4000X + Y = 660
Week 2: 6000X + Y = 740
Now, I am going to subtract the above equations like so (to help solve for X and Y):
6000X + Y = 740
– (4000X + Y = 660)
2000X = 80
(notice how the Y’s disappeared?? Good news)
So, now solve for X:
2000X = 80
X = 80/2000 = .04
So, now we know X = .04. We need to use that info to solve for Y in either equation (1) or (2) from above… I will pick equation (1):
4000X + Y = 660
Now plug in X = .04:
4000(.04) + Y = 660
160 + Y = 660
Y = 500
So, Steve earns $500 as salary and has a commision rate of .04 (which is 4%).
Thank you so much! This helped a lot!
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