Question

Sara is moving into a new apartment. The Resort complex charges a $600 security

Answer 1

Answer:

The rent is the same when 2 months have passed.

If she'd live in them for 6 months, I'd recommend the resort complex, since it'd be cheaper.

Step-by-step explanation:

Sara has two options, the resort complex and the uptown suites duplex, which can be represented by functions where "c" is the cost and "t" is the number of months Sara lives on each apartment.

The Resort complex:

$c_{resort}(t) = 600 + 950*t$

The Uptown Suites Duplex:

$c_{uptown}(t) = 300 + 1100*t$

To find the number of months she has to live in them in a way that they have the same cost, we need to find the value of t that makes both equations equal, this is done below:

$600 + 950*t = 300 + 1100*t\\1100t - 950t = 600 - 300\\150t = 300\\t = \frac{300}{150} = 2$

The rent is the same when 2 months have passed.

If she intends to live in them for 6 months, the cost of each are:

$c_{resort}(t) = 600 + 950*6 = 6300$

$c_{uptown}(t) = 300 + 1100*6 = 6900$

If she'd live in them for 6 months, I'd recommend the resort complex, since it'd be cheaper.