Word Problem

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%).

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