Having trouble with a math problem

Question

A local salesman receives a base salary of $575 monthly. He also receives a commission of 9% on all sales over $1950. How much would he have to sell in a month if he needed to have a monthly income of $2700?



Answer 1

We know that the base salary of $575/mo. is not based on commission and can simply be added to the equation. So the question is, how many $1,950 sales does the salesman have to make for his/her 9% commission to equal $2,700.

Let's write it like this: 2,700 = 575 + (1,950*0.09)X

where $2,700 is the goal monthly salary and it equals the individual base salary of $575 plus the 9% commission on sales over $1,950 multiplied by X which represents the number of sales he or she has to make to attain the goal. Now, just solve for X!

2,700 = 575 + 175.5X

*(subtract 575 from both sides)

2,125 = 175.5X

*(divide both sides by 175.5)

X = 12.1

Since the value is not an integer and likely he or she cannot sell 0.1 items, the salesman should seek to sell 13 items of greater value than $1,950 per month based on the 9% commission if they wish to have a monthly salary of $2,700.

Thanks!