sofia wants to rent an apartment. she visits apartment a which charges $100 for a one time deposit and $400 per month for rent. she visits apartment b which charges $500 for 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.

Given that one time charge of appartment "a" = $100Given that monthly rent of appartment "a" = $400say the number of months = xthen total cost of the rent for apartment "a" = 100+400x
Given that one time charge of appartment "b" = $500Given that monthly rent of appartment "b" = $350then total cost of the rent for apartment "b" = 500+350x
Now we have to make an inequality so that number of months it would take for the total paid to be less for apartment b.that means 100+400x is less than 500+350x
Hence required inequality is 100+400x<500+350x.
Now we have to solve this inequality.400x-350x<500-10050x<400divide both side by 50x<8hence final answer is number of months should be less than 8.