Question

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 8% of your sales


Option B: Base salary of $24,000 a year, with a commission of 4% of your sales


In order for option A to produce a larger income, you would need sell at least $

of jewelry each year.

Answer 1

$175,000

Explanation:

We can use a system of inequalities to solve this problem

Let X be the sales of jewelry in $

Option A

Base salary = $17,000
Commission: 8% of sales

Commission at 8% =8% x $X = 8/100 x $X = $0.08X

Total remuneration = 17,000 + 0.08X

Option B

Base salary = $24,000

Sales = X$

Commission = 4% of $X = 4/100 x $X = $0.04X

Total remuneration = 24,000 + 0.04X

For Option A to be a better deal(higher income)
Total remuneration on Option A > Total remuneration on Option B

17,000 + 0.08X ≥ 24,000 + 0.04X

(we are using ≥ symbol though the question does state larger income, later on it states at least how many $ worth of sales)

Subtract 0.04X from both sides:
17,000 + 0.08X - 0.04X >= 24,000 + 0.04X -0.04X

17,000 + 0.04X >= 24,000

Subtract 17,000 both sides:
17,000 - 17,000 + 0.04X ≥ 24,000 - 17,000

0.04X ≥ 7,000

X ≥7000/0.04

X ≥ $175,000

So under Option A, you would need to sell at least $175,000 worth of jewelry to make a larger income.

Actually at $175,000 the income from both options are equal