When hired at a new job selling jewelry, you are given two pay options:
option a: base salary of $17,000 a year, with a commission of 12% of your sales
option b: base salary of $20,000 a year, with a commission of 5% of your sales
how much jewelry would you need to sell for option a to produce a larger income?

Explanation:

To find the amount of sales for option A to produce a larger income, first find a model for both options.

Firstly ,Let A(s) be the salary in dollars produced per year from option A .

Since the salary increases by 12 cents for each additional dollar in sales, A(s) is a linear function with a rate of change, or slope, of .12

The initial value is the base salary per year or $17000

There the linear model is A(s) = 0.12s + $17000(1).

Secondly ,Let B(s) be the salary in dollars produced per year from option B by selling

Since the salary increases by 5 cents for each additional dollar in sales, B(s) is a linear function with rate of change, or slope, of .05.

The initial value is the base salary per year or $20000.0 .The linear model is B(s) = 0.05s + $20,000(2)

To find the sales needed so that the salary from option A is greater than option B, find the set of s-values that make the output values from equation (1) greater than the output values from equation (2) .

A(s) = 0.12s + $17000 > B(s) = 0.05s + $20,000

0.12s + $17000 >0.05s + $20,000

0.12s- 0.05s > $20,000-$17000

0.07s >$3000.00

Therefore s > $42,857.14

Therefore, more than $42,857.14 would need to be sold for option A to produce a larger income than option B.