Question

I=0.5(18+m)

A landlord determines that the total amount of income, I, in thousands of dollars generated by renting out a home is given by the equation above. Negative values of m represent the time m months before January 1, 2010 and positive values of m represent the time m months after January 1, 2010. The landlord had an income of 0 when the home was bought and only began receiving income from rent afterward. When did the landlord buy the home?

A) The landlord bought the house 18 months before January 1, ... 2010.
B) The landlord bought the house 9 months before January 1, 2010.
C) The landlord bought the house 9 months after January 1, 2010.

Answer 1

The landlord bought the house 18 months before January 1, 2010, as indicated by solving the equation I = 0.5(18 + m) for when I equals 0, giving the value m = -18.

Step-by-step explanation:

The equation given, I = 0.5(18 + m), represents the total income, I, in thousands of dollars that a landlord makes from renting a house, depending on the time m in months before or after January 1, 2010. The question is asking us to determine when the landlord bought the house, based on the information that the income started at 0.

To solve this, we need to find the value of m when I equals 0:

• First, we understand that the income I was 0 at the point of purchase.
• Next, we set the equation equal to 0 and solve for m: 0 = 0.5(18 + m).
• Multiplying each side by 2 to eliminate the coefficient of the parenthesis, we get: 0 = 18 + m.
• Lastly, solving for m, we find that m = -18, which means that the landlord bought the house 18 months before January 1, 2010.

Therefore, the correct answer is A) The landlord bought the house 18 months before January 1, 2010.