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?

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.

Step-by-step 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.