Answer:
Justin's salary is $400/month. His commission is 25% of his sales.
Step-by-step explanation:
Let y be Justin's income for one month. His salary is made up of a monthly base pay, which we'll call x, and a commission on the sales, S, he makes in that month. We will assume the commission is a fixed ratio of sales every month, which we will call b. b is the percentage his commission is based on.
Justin's total monthly salary is therefore:
y = x + b(S)
where y is monthly salary, x is monthly base pay, b is the rate of commission, and S are his merchandise sales in that month.
We are told in one month Justin earned a total of $500 in a month he sold $400 of merchandise.
We have y = $500, and S = $400, so we can write:
500 = x + b(400)
In another month, Justin earns a total of $575 when he sold $700 of merchandise. We can write:
575 = x + b(700)
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We have two unknowns (x and b) and two equations. If we substitute one equation into another, we will eventually find the values of x and b.
Take the first equation and rearrange it to isolate x:
500 = x + b(400)
x = 500 - b(400)
Now take the second equation and substitute this definition of x:
575 = x + b(700)
575 = (500 - b(400)) + b(700)
575 = 500 + 300b
75 = 300b
b = (75/300)
b = 0.25
The rate of commission Justin receives on the merchandise he sells is 0.25 or 25%. Nice.
575 = x + b(700)
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Now take either equation and set b = 0.25, then solve for x, Justin's monthly base pay:
575 = x + b(700)
575 = x + (0.25)(700)
575 = x + 175
x = 400
Justin's base pay is $400/month.
CHECK
Do the values of x ($400) and b(0.25) result in the pay amounts for the months discussed?
y = $400 + (0.25)b
Month Sales(S) Base Pay Commission (0.25)*(S) Total($) Actual($)
1 400 400 (0.25)*(400)= $100 $500 $500
2 700 400 (0.25)*(700)= $175 $575 $575
These values work.
