Question 1115878: a sales man earns aweekly basic salary plus a sales commision of 20% of his total sales when his total weekly sales are birr 1000,this total salary for the week is 400.drive the formula describing th erelationship between total salary and sales?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! his total compensation is equal to s + c.
s is his salary.
c is his commission.
t is his total compensation.
the formula becomes t = s + c
when c = .20 * merchandise sold, the formula becomes t = s + .20 * m, where m is themerchandise sold.
when he makes 400 and sells 1000 worth of merchandise, the formula becomes 400 = s + .20 * 1000
simplify this to get 400 = s + 200
subtract 200 from both sides of this equation to get 400 - 200 = s
solve for s to get s = 200.
the salary will be the same every week.
what will be different is the commission.
for example, if they sell 2000 worth of merchandise each week, then the formula becomes t = 200 + .20 * 2000.
this results in t = 200 + 400 = 600.
total compensation for the week will then be 600 rather than 400.
backtracking and solving for s, you get 600 = s + .20 * 200 which results in 600 = s + 400 which results in s = 200.
you're asked to derive the formula describing the relationship between totel salary and sales.
that formula, based on the variables used here, would be t = s + .2 * m, where t = total compensation and s equal weekly salary and m = value of merchandise sold and .2 is the proportion of total merchandise sold that goes to the salesman.
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