Question

When hired at a new job selling jewelry, you are given two pay options: Option A: Base salary of

$16,000 a year, with a commission of 12% of your sales Option B: Base salary of
$26,000 a year, with a commission of 5% 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

$142,857.143

Explanation:

set you need sell at least $x to make option A to prodece a larger income,

16,000+0.12x>26,000+0.05x

16,000-26,000>0.05x-0.12x

-10,000>-0.07x

x>142,857.143

Answer 2

$142,858

Explanation:

You want to know the sales amount that would give a salary option of $16,000 in base pay with a 12% commission a larger income than a salary option of $26,000 in base pay with a 5% commission.

Income

Your income in each salary plan is ...

plan A = 16000 +0.12s . . . . . . for s dollars in sales

plan B = 26000 +0.05s

Comparison

For plan A to produce a greater income than plan B, you want ...

plan A > plan B

16000 +0.12s > 26000 +0.05s

0.07s > 10000 . . . . . . . . subtract 16000+0.05s

s > 142857.1429

You would need to sell at least $142,858 of jewelry each year.

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Additional comment

We have rounded up to the nearest dollar, so that this amount of sales will result in a larger income under plan A. If we were to round (down) to dollars or to cents, the amount would actually give a smaller income under plan A.