Question

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

deposit and costs $950 a month for rent. The Uptown Suites Duplex charges a $300
security deposit and costs $1100 a month for rent. After how many months would the
apartments cost the same amount? Which apartment would you recommend Sara move
to if she plans on staying for 6 months? Please show work.

Answer 1

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.

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 = (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.