Credit To: "lublana" For This Answer
Answer:
For apartment "a", the one-time fee is $100.
The monthly rent for apartment "a" is $400.
Let’s denote the number of months as x.
Thus, the total cost for renting apartment "a" can be expressed as: 100 + 400x.
For apartment "b", the one-time fee is $500.
The monthly rent for apartment "b" is $350.
Therefore, the total cost for renting apartment "b" becomes: 500 + 350x.
We need to set up an inequality indicating how many months it would take for the total expense to be lower for apartment b.
This translates to: 100 + 400x is less than 500 + 350x.
Consequently, the required inequality is: 100 + 400x < 500 + 350x.
Now, let’s solve the inequality.
Subtracting gives us: 400x - 350x < 500 - 100.
Which simplifies to: 50x < 400.
Dividing both sides by 50 results in: x < 8.
Conclusively, the total months must be less than 8.
