Question

Mr. Nordman gets a commission of $2.30 on each pair of women's shoes he sells, and a commission of $3 on each pair of men's shoes he sells. To meet his sales targets, he must sell at least 10 pairs of women's shoes and at least 5 pairs of men's shoes. He also wants to make at least a $60 a week in commissions. Define the variables, write a system of inequalities to represent this situation, and name one possible solution.

Answer 1

x ≥ 5

y ≥ 10

3x + 2.3y ≥ 60

Explanation:

Lets the number of men's shoes he sells be x and women's shoes be y.

For each men's shoes , he gets a commission of $3 and for each women's shoe, he gets a commission of $2.30 .

He needs to sell atleast 10 women's shoes and 5 men's shoes.

Also he needs to make atleast $60 per week.

x ≥ 5

y ≥ 10

3x + 2.3y ≥ 60

These are are the 3 required inequalities.

Now we will see an example.

If he sells 20 womens shoes and 10 mens shoes , he will meet the requirements.

He will make a total profit =
`2.3* 20 + 3* 10` =$76