Sabrina is contemplating a job switch. She is . . . .

Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission for each sale made. If each of her sales is for $1,500, what is the least number of sales she must make per year if she is not to lose money because of the job change?

A) 57
B) 177
C) 178
D) 377
E) 378

The OA is the option C.

How can I calculate the correct answer here? Experts, can you help me? I'd be thankful.

Hi M7MBA,
Let's take a look at your question.

Old job paid Sabrina annually = $85,000
New job pays $45,000 plus 15% commission of each sale.
If each sale is for $15,000, then commission earned by each sale will be:
$$=15000\times15\%$$
$$=15000\times\frac{15}{100}=225$$

Let Sabrina make 'x' sales per year, then to avoid losing money due to job change, her yearly income including commission should be more than $85,000.
It can be written as:
$$45,000+225x>85,000$$
$$225x>85,000-45,000$$
$$225x>40,000$$
$$x>\frac{40000}{225}$$
$$x>177.78$$

Since x is the number of sales, it can not be decimal so we will round it off to a whole number.
Hence to avoid losing money due to job change, Sabrina has to make at least 178 sales per year.

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.