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Irina-Kira
2 months ago
11

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 also visits Apartment B which charges $500 for a 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.
Mathematics
1 answer:
babunello [11.8K]2 months ago
6 0

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.

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Detailed explanation:

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