Question

A real estate company offered two plans to a new employee: Plan A is a salary of $2500 per month plus a 6% commission on sales. Plan B is a salary of $3000 per month plus a 4% commission on sales. For what amount of monthly sales is Plan A better than Plan B? Set up an inequality and show all work to solve the inequality

A. $30,000
B. $40,000
C. $50,000
D. $60,000

Answer 1

Plan A is better than Plan B when monthly sales exceed $30,000. We found this by setting up an inequality to compare both plans' earnings and solving for the sales amount where Plan A surpasses Plan B.

Step-by-step explanation:

To determine for what amount of monthly sales Plan A is better than Plan B, we set up an inequality comparing the total earnings from both plans. Plan A's earnings can be represented by the equation 2500 + 0.06x, where x is the monthly sales, while Plan B's earnings can be represented by the equation 3000 + 0.04x.

We want to find out when Plan A's earnings are greater than Plan B's earnings, so we set up the inequality:

2500 + 0.06x > 3000 + 0.04x

Now we'll solve for x:

Step 1: Subtract 2500 from both sides of the inequality to isolate the variable terms:

0.06x > 500 + 0.04x

Step 2: Subtract 0.04x from both sides to get all x terms on one side:

0.02x > 500

Step 3: Divide both sides by 0.02 to solve for x:

x > 25000

This means that Plan A is better than Plan B when the monthly sales exceed $25,000. Looking at the options provided, the next highest option above $25,000 is $30,000 (Option A). Therefore, Plan A will be better for the employee when monthly sales exceed $30,000.