Question

You are a salesperson at the local Nissan dealer. Each month you earn $2,200 plus one-fifteenth of your sales. You want to earn more than $4,000 this month. How much must you sell this month in order to earn more than $4,000? Use an inequality to solve this problem.

Answer 1

In order to earn more than $4,000 in a month, a salesperson who makes $2,200 base salary plus one-fifteenth of their sales must sell more than $27,000 worth of cars.

Step-by-step explanation:

To determine how much you must sell this month to earn more than $4,000, you can set up and solve an inequality. Let's denote your monthly sales as S.

Your earnings are composed of a base salary and a commission. The problem states that you earn $2,200 plus one-fifteenth of your sales. Let's express this as:

Earnings = Base Salary + Commission

Or mathematically:

Earnings = $2,200 + ⅓S

You want to earn more than $4,000, so we set up the inequality:

$2,200 + ⅓S > $4,000

Now, solve for S:

1. 
   
3. Subtract $2,200 from both sides of the inequality to isolate the commission term:
   ⅓S > $4,000 - $2,200
4. 
   
6. Simplify the right side: ⅓S > $1,800
7. 
   
9. To find S, multiply both sides by 15:
   S > 15 × $1,800
10. 
    
12. Solve for S:
    S > $27,000

You would need to sell more than $27,000 worth of cars this month to earn more than $4,000.