An electronics store offers its employees two different compensation plans. Employees on plan A earn $500 per week plus a 25% commission on their weekly sales of the products. Employees on Plan B earn $750 per week plus a 15% commission on their weekly sales of the products. Which inequality describes the amount in sales each week, x dollars, for which employees on plan A earn more than employees on Plan B? A)x<1250 B)x>1250 C)x<2500 D)x>2500
Could you please write down the calculating procedures? Thanks a lot.
Plan A
earnings = 500 + .25x
Plan B
earnings = 750 + .15x , where x is the amount of sales in each case
When is PlanA > PlanB ?
500 + .25x > 750+.15x
.1x > 250
x > 2500
Well, well! Looks like the employees have quite the deal going on! Now, let's see which bunch of employees will be laughing all the way to the bank!
For employees on Plan A, the total compensation is $500 per week plus a 25% commission on their sales.
So for the total compensation, we can write the equation: Total compensation for Plan A = $500 + (0.25)(x), where x is the amount of weekly sales in dollars.
For employees on Plan B, the total compensation is $750 per week plus a 15% commission on their sales.
So for the total compensation, we can write the equation: Total compensation for Plan B = $750 + (0.15)(x), where x is the amount of weekly sales in dollars.
Now, to figure out when Plan A is better than Plan B, we want to find the amount in sales, x dollars, for which employees on Plan A earn more than employees on Plan B. In other words, we want to find the value of x for which
Total compensation for Plan A > Total compensation for Plan B.
So we can write our inequality as:
$500 + (0.25)(x) > $750 + (0.15)(x).
To solve this inequality, let's start by subtracting $500 from both sides to isolate the x term:
(0.25)(x) - (0.15)(x) > $750 - $500.
Simplifying further:
(0.1)(x) > $250.
Now, to get rid of the 0.1 coefficient, we divide both sides of the inequality by 0.1:
x > $2500.
Voila! The inequality that describes the amount in sales each week, x dollars, for which employees on Plan A earn more than employees on Plan B is x > $2500.
So, my friend, if the weekly sales exceed $2500, employees on Plan A will be grinning from ear to ear while their Plan B counterparts might just be clowning around! Keep those sales booming!
To determine the amount in sales each week, x dollars, for which employees on Plan A earn more than employees on Plan B, we need to compare the total earnings for each compensation plan.
For Plan A:
Earnings on Plan A = $500 + 25% of weekly sales
= $500 + (0.25x)
For Plan B:
Earnings on Plan B = $750 + 15% of weekly sales
= $750 + (0.15x)
Now, we need to find when the earnings on Plan A are greater than the earnings on Plan B. Mathematically, this can be represented as:
500 + 0.25x > 750 + 0.15x
To simplify the inequality, we can subtract 0.15x from both sides:
0.25x - 0.15x > 750 - 500
0.1x > 250
Divide both sides of the equation by 0.1:
x > 2500
Therefore, the correct inequality is x > 2500. This means that for weekly sales above $2500, employees on Plan A will earn more than employees on Plan B.
To determine the inequality that describes the amount in sales each week, x dollars, for which employees on plan A earn more than employees on plan B, we need to compare the earnings of the two compensation plans.
Let's break down the earnings for each plan:
Plan A: $500 + 25% of weekly sales
Plan B: $750 + 15% of weekly sales
To find the amount in sales, x dollars, for which plan A earns more than plan B, we can set up the following inequality:
(500 + 0.25x) > (750 + 0.15x)
Now, let's solve the inequality step by step:
1. Subtract 0.15x from both sides:
500 + 0.25x - 0.15x > 750
0.10x > 250
2. Divide both sides by 0.10:
x > 2500
Therefore, the inequality that describes the amount in sales each week, x dollars, for which employees on plan A earn more than employees on plan B is:
x > 2500
The correct answer is D) x>2500.