Apartment a charges $200 for one-time deposit and $400 per month for rent. Apartment b charges $500 for a deposit, but only charges $350 per month in rent. Write in inequality that would determine how many months it would take for cumulative amount paid to be less for apartment b

sofia wants to rent an apartment. she visits Apartment a charges $200 for one-time deposit and $400 per month for rent. Apartment b charges $500 for a deposit, but only charges $350 per month in rent. Write in inequality that would determine how many months it would take for cumulative amount paid to be less for apartment b

APARTMENT "A"

✓From the question, the one time charge of appartment "a" = $200

and the monthly rent of the appartment = $400

✓ Let denote the number of months as " y"

We can find the TOTAL COST of the rent for apartment "a" as( 200+400y)

TOTAL COST= (200+400y)

APARTMENT "B"

From the question, the one time charge of the appartment is given as $500,The monthly rent of the appartment is given as $350

The total cost of the rent for the apartment can be expressed as (500+350y)

We need to write and solve an inequality that shows how many months it would take for the total paid to be less for apartment b.

Then the total cost of apartment "a" is less than "b" we can expressed it as;

200+400y<500+350y

Collect like terms, we have

400y-350y<500-200

50y<300

y<6

Hence, it takes less than 6 months it would take for the total paid to be less for apartment b.