SOLUTION: An apartment building contains 200 apartments. Some apartments have only one bedroom and rent for $435 per month. The rest have two bedrooms and rent for $575 per month. When all t

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Question 230561: An apartment building contains 200 apartments. Some apartments have only one bedroom and rent for $435 per month. The rest have two bedrooms and rent for $575 per month. When all the units are rented, the total monthly income is $97,500. How many two-bedroom apartments are there?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
An apartment building contains 200 apartments. Some apartments have only one bedroom and rent for $435 per month. The rest have two bedrooms and rent for $575 per month. When all the units are rented, the total monthly income is $97,500. How many two-bedroom apartments are there?

Step 1. Let x be the number of one-bedroom apartments

Step 2. Let 200-x be the number of two-bedroom apartment since there are a total of 200 apartments.

Step 3. Let 435x be the monthly dollar value of one-bedroom apartments.

Step 4. Let 575(200-x) be the monthly dollar value of two-bedroom apartments.

Step 5. Then, 435x%2B575%28200-x%29=97500 be the total monthly dollar value.

Step 6. Solving 435x%2B575%28200-x%29=97500 yields the following steps

435x%2B115000-575x=97500

-140x%2B115000=97500

Add 140x to both sides of the equation

-140x%2B115000%2B140x=97500%2B140x

115000=97500%2B140x

Subtract 97500 from both sides of the equation

115000-97500=97500%2B140x%2B97500

17500=140x

Divide 140 to both sides of the equation

17500%2F140=140x%2F140

x=125 and 200-x=75

Check total monthly value: 125%2A435%2B75%2A575=54375%2B43125=97500 which is a true statement.

Step 7. ANSWER: The number of two-bedroom apartments is 75.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J