Question

Sophia want to rent an apartment she visits apartment A Whitehall charges $100 for a one time deposit and $400 per month for rent she also visits apartment B whatcha charges $500 for a deposit but only charges $350 per month in rent write and solve an inequality that shows how many months it would take for the total paid to be less for apartment B?

Answer 1

The inequality in this case is 100 + 400*t > 500 + 350*t and for B to be cheaper Sophia has to rent it for more than 8 months.

Explanation:

In order to write the inequality we first need to write two equations one for each apartment. For apartment A we have a fixed cost of $100 and a variable cost of $400 that varies according to the time living in there, so we have:

rent = 100 + 400*t

For apartment B we have a fixed cost of $500 and a variable cost of $350 that varies according to the time living in there, so we have:

rent = 500 + 350*t

In order for the total paid in B to be less than for the one in A we need to satisfy the following inequality:

100 + 400*t > 500 + 350*t

400*t - 350*t > 500 - 100

50*t > 400

t > 400/50

t > 8 months

The inequality in this case is 100 + 400*t > 500 + 350*t and for B to be cheaper Sophia has to rent it for more than 8 months.