Question

Write an inequality to determine when Apartment A will cost more than Aparment B: Johnny is searching for an apartment and has narrowed it down to two choices. Apartment A has a $300 security deposit and costs $800 each month. Apartment B has a $900 deposit and costs $500 each month.

Answer 1

Apartment A will cost more than Aparment B after 2 months which means from the third month and above, Apartment A will cost more than Aparment B

Explanation:

Write

Let the number of months be represented as y

Apartment A has a $300 security deposit and costs $800 each month.

$300 + $800 × y

300 + 800y

Apartment B has a $900 deposit and costs $500 each month

$900 + $500 × y

900 + 500y

An inequality to determine when Apartment A will cost more than Aparment B :

Apartment A > Apartment B

300 + 800y > 900 + 500y

300 + 800y = 900 + 500y

Collect like terms

800y - 500y = 900 - 300

300y = 600

y = 600/300

y = 2 months

Therefore Apartment A will cost more than Aparment B after 2 months which means from the third month and above, Apartment A will cost more than Aparment B