As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
50 + 3s >100
100 - 3s ≤ 160; s ≤ 20
50+3x≥100
Explanation:
You will always have the given $50 earned per week, then you add a variable to represent the theoretical amount of sales per that week. Then, you add the ≥100 (greater than 100) to show that the sales earned for that week plus the additional $50 per week must at least $100.
To write an inequality for the number of sales you need to make, let's define the number of sales as "s".
Given that you are paid $50 per week plus $3 per sale, we can express your total pay as:
Total Pay = $50 + ($3 x number of sales)
To ensure your pay is at least $100, we can write the following inequality:
Total Pay ≥ $100
Substituting the expression for total pay, we get:
$50 + ($3 x s) ≥ $100
To solve this inequality, we can begin by isolating the variable "s".
First, we subtract $50 from both sides of the inequality:
$3s ≥ $100 - $50
$3s ≥ $50
Next, we divide both sides of the inequality by 3:
s ≥ $50 / $3
s ≥ 16.67
Since you cannot have a fraction of a sale, we round up to the nearest whole number. Therefore, you would need to make at least 17 sales to ensure your pay is at least $100.
The solutions to the inequality are all whole numbers greater than or equal to 17.