Question

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.

Answer 1

Given that one time charge of appartment "a" = $100

Given that monthly rent of appartment "a" = $400

say the number of months = x

then total cost of the rent for apartment "a" = 100+400x

Given that one time charge of appartment "b" = $500

Given that monthly rent of appartment "b" = $350

then 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<500-100

50x<400

divide both side by 50

x<8

hence final answer is number of months should be less than 8.