Name: Jay B.

Who is asking: Student

Level: Middle

Question:
My math teacher gave us this Algebra problem: Ron the realtor is offered a job directly out of real-estate school. He has a choice as to which way he will receive his salary the first year.

Salary Plan 1: He would receive a base pay of $2000 per month plus a 3% commission on each sale.

Salary Plan 2: No base pay but a 6% commission on each sale. Write an equation to determine when it would be better to switch from the first plan to the second plan. Give a one- or two-sentence answer that includes Ron`s sales in a month. Round to the nearest dollar, if necessary.

I can`t seem to figure out how to approach this problem. I thought about graphing it as a function, but can`t seem to figure out how. I`M LOST! PLEASE HELP! This is due February 23, 2001, I would appreciate your prompt response. Thank you very much. -Jay

Hi Jay,

Graphing is not a bad idea. First I looked at some numbers. Suppose that he sold $100 000 worth of real-estate in one month. How much would he make?

Salary Plan 1: He would receive $2000 plus 3% of $100 000, that is $2000 + $3000 = $5000.

Salary Plan 2: He would receive 6% of $100 000 or $6000 Hence in this case salary plan 2 is better.

Suppose he sold $50 000 worth of real-estate. How much would he make?

Salary Plan 1: He would receive $2000 plus 3% of $50 000, that is $2000 + $1500 = $3500.

Salary Plan 2: He would receive 6% of $50 000 or $3000 In this case salary plan 1 is better.

The question to ask is "How much real-estate sold would result in salary plans 1 and 2 giving the same result?" If he sells $x then salary plan 1 results in $2000 plus 3% of $x and salary plan 2 results in 6% of $x. Thus find x if $2000 plus 3% of $x equals 6% of $x.

Cheers,
Penny

Here is a second answer from Leeanne

Hi Jay,

You were on the right track with your idea about graphing, but you would need to graph 2 functions not just one. Set up a coordinate plane with your x-axis being monthly sales and the y-axis being monthly salary. Now if you graph each of the functions that represent each of the salary options available (hint: use a different colour for each line, say red abnd blue) you should be able to divide the graph into two sections: (1) the part where the red line is above the blue line - for these x-values (monthly sales amounts) the salary option representing the red line is better. (2) the part where the blue line is above the red line - the salary option representing the blue line is better.

At the point where the two lines cross, there is no difference between the two salary options.

There is also a way to solve this problem with only algebra. Suppose we want to find out the monthly sales figure the employee has to reach in order for the 6% commission option to be the better option. If we let x be the unknown monthly sales figure, the we need to solve the following inequality for x:

6% of x is greater than 2000 plus 3% of x

The answer to this inequality will tell you range or interval of monthly sales figures that will yield a higher salary under the option of taking only 6% commission.

Hope this helps,

Leeanne

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