Suppose you work in a clothing store. Each week you earn $250 plus a commission equal to 2.5% of your sales. This week your goal is to earn no less than $350. Write and solve an inequality to find the amount of sales you must have to reach your goal.

Question

Suppose you work in a clothing store. Each week you earn $250 plus a commission equal to 2.5% of your sales. This week your goal is to earn no less than $350. Write and solve an inequality to find the amount of sales you must have to reach your goal.

Answer 1

To find the amount of sales you must have to reach your goal, let's do the following steps:

Step 1: Convert the problem into an inequality.
Let's define "x" as the amount of sales you make this week. The commission you earn will be 2.5% of your sales, which is equal to (0.025 * x). The inequality to represent your goal of earning no less than $350 can be written as:
250 + (0.025 * x) ≥ 350

Step 2: Simplify the inequality.
Combine like terms to simplify the inequality:
250 + 0.025x ≥ 350

Step 3: Isolate the variable.
To isolate the variable "x," we need to subtract 250 from both sides of the inequality:
0.025x ≥ 350 - 250
0.025x ≥ 100

Step 4: Solve for x.
To solve for x, divide both sides of the inequality by 0.025:
x ≥ 100 / 0.025
x ≥ 4000

Step 5: Interpret the solution.
The solution to the inequality is x ≥ 4000. This means you must have made at least $4000 in sales to reach your goal of earning no less than $350 this week.

Therefore, to reach your goal, you must have at least $4000 in sales.

Answer 2

Let's represent the amount of sales as 'x'.

According to the given information, the commission you earn on sales is 2.5% of the sales amount. So, the commission earned can be calculated as 0.025x (2.5% is equivalent to 0.025 as a decimal).

To reach a goal of earning no less than $350, we can write the following inequality:

$250 + 0.025x ≥ $350

Now, let's solve the inequality:

$250 + 0.025x ≥ $350

Subtract $250 from both sides:

0.025x ≥ $100

To isolate 'x', divide both sides of the inequality by 0.025:

x ≥ $100/0.025

Simplifying further:

x ≥ $4000

Therefore, to reach your goal of earning no less than $350, you must have sales of at least $4000.

Answer 3

p=pay, s=sales

p = 250 + .025s

you want at least 350 pay

p >= 350
250 + .025s >= 350
.025s >= 100
s >= 4000

so, sell at least $4000 -- get busy!