word problems

Question

a salesperson receives a monthly salary $2000 plus commission of 7% of sales. she is offered a new job at $2300 per month plus commission of 5% os sales.
a) write a linear equation for her current wage W in terms of her monthly sales S.
b)write a linear equation for her monthly wage W of the job offer in terms of her monthly sales S.
c) what level of sales will make her indifferent between the two jobs?which scheme is preferred when sales are below this level?

Answer 1

a)   W_c = 2000+.07S

 

b)  W_n =2300+.05S

 

c)  The level of sales at which she would be indifferent

     would when the totals are equal

    2000 + .07S = 2300 + .05S

    subtract .05S from both sides

     2000 +.02S = 2300

    subtract 2000 from both sides

     .02S = 300

    divide both sides by .02

    S = 300/.02 = 15000

 

When sales are $15,000 the wages are equal

 

When S < 15,000 which plan earns more money?

 

If we work the same equation, replacing the = sign

with less than < ... Our equation works out to

 

2000 + .07S < 2300 + .05S

S < 15000

 

When sales are less than $15,000 then the current

job earns less than the new offer.  Thus, for sales

under $15,000 the new job offer is preferable.

 

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check:  Let S = 10,000

W_c = 2000+.07(10000) = $2700

W_n = 2300 + .05(10000) = $2800

 

As can be seen, at sales of $10,000 the new job earns more.