Math CentralQuandaries & Queries


Subject: equations
Name: kathy
Who are you: Student

patrick has been offered jobs by two different automobile repair shops. his income from the first shop will be $1,200 per month plus 3% of the monthly sales. the second shop will pay patrick $1,500 per month plus 2% of the monthly sales.

part a let s equal the amount of monthly sales and i equal patrick's income in dollars. write a system of two equations that could be used to determine the monthly income from either shop.

part b solve the equation to determine what amount of monthly sales for each shop would result in patrick earning the same monthly income, i, from both shops

Hi Kathy,

A third shop that wants to encourage really aggressive sales people also offers Patrick a job which will pay $800 per month plus 10% of his monthly sales. Let i3 be his monthly income if he accepts this job and s the amount of his monthly sales. In this situation Patrick's income will be $800 plus 10% of s, that is

i3 = 800 + 0.10 s

Let i1 be Patrick's income if he accepts the job at the first shop and i2 be his income if he accepts the job at the second shop. Find expressions like I did above for i1 and i2.

Part b asks if i1 = i2 what is s?


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