Question

Apartment A requires 1000 security deposit and costs 1200 each month apartment B has a 1500 security deposit and costs 1175 each month at how many months m will apartment A be less than apartment B?

Answer 1

Apartment A will be less expensive than Apartment B for any period of time less than 20 months. The total costs for both apartments are compared to determine when Apartment A becomes less expensive.

Step-by-step explanation:

To determine at how many months m Apartment A will be less expensive than Apartment B, we need to establish the total cost equations for both apartments over time and find the point where the cost of Apartment A is less than the cost of Apartment B.

Let's denote m as the number of months. The total cost for Apartment A after m months is:
Total Cost A = Security Deposit + (Monthly Rent × Number of Months)
Total Cost A = $1000 + ($1200 × m)

The total cost for Apartment B after m months is:
Total Cost B = Security Deposit + (Monthly Rent × Number of Months)
Total Cost B = $1500 + ($1175 × m)

We then set up an inequality to solve for m when Total Cost A < Total Cost B:
$1000 + ($1200 × m) < $1500 + ($1175 × m)

To find the solution, we subtract $1175m and $1000 from both sides:
$1000 + $25m < $1500
$25m < $500

Dividing by $25 gives us the value of m:
m < 20

Therefore, Apartment A will be less expensive than Apartment B for any period less than 20 months.