Question

A local salesman receives a base salary of $925 monthly. He also receives a commission of 6% on all sales over $1700. How much would he have to sell in a month if he needed to have a monthly income of $2600?

Answer 1

To have a monthly income of $2600, the salesman needs to make total sales of $29,616.67, considering his base salary of $925 and a 6% commission for sales over $1700.

Step-by-step explanation:

The question asks us to calculate how much a local salesman needs to sell to have a monthly income of $2600. The salesman receives a base salary of $925 and earns a commission of 6% for all sales over $1700.

To solve this, we need to figure out the total sales that would give the salesman an extra $1675 ($2600 total desired income minus the $925 base salary), knowing that he only gets a commission on the amount over $1700.

Let's denote the total amount in sales that the salesman needs to make as S.

The commission is only applied to the amount exceeding $1700, so the equation can be set up as follows:

• 0.06(S - $1700) = $1675.

• Solving this equation, we find that S - $1700 = $1675 / 0.06, which means S - $1700 = $27,916.67.

• Adding $1700 to both sides, we get S = $27916.67 + $1700, which equals $29,616.67.

Therefore, the salesman would need to sell $29,616.67 worth of goods in a month to have a total monthly income of $2600.

Answer 2

$29,616.67

Step-by-step explanation:

monthly salary = fixed part + commission part

The fixed part is $925.

The commission part is 6% on all sales over $1700.

Let x = amount of sales, and x must be greater than $1700.

Then, the amount of sales over $1700 is x - 1700.

He earns 6% on that amount, so the commission part is 6%(x - 1700),

or 0.06(x - 1700).

monthly salary = fixed part + commission part

monthly salary = 925 + 0.06(x - 1700)

925 + 0.06(x - 1700) = 2600

0.06(x - 1700) = 1675

0.06x - 102 = 1675

0.06x = 1777

x = 29,616.67

Answer: $29,616.67