Question

A contractor is building an apartment complex with the following specifications: there will be 210 apartments with one, two, or three bedrooms. One-third of the apartments will have two bedrooms. There will be three times as many one-bedroom apartments as three-bedroom apartments. Which of the following statements are true about the apartment complex? Select either true or false next to each statement.

1) One-third of the apartments will have three bedrooms.
2) There will be 70 one-bedroom apartments.
3) There will be 30 two-bedroom apartments.
4) There will be 10 three-bedroom apartments.

Answer 1

Using arithmetic and the relationships given, it is determined that there are 70 two-bedroom apartments, 105 one-bedroom apartments, and 35 three-bedroom apartments, making all the provided statements false.

Step-by-step explanation:

Given the specifications for an apartment complex with 210 apartments divided into one, two, and three-bedroom units, we can determine the truth of the following statements by applying some basic math:

1. One-third of the apartments will have three bedrooms - False, because the apartments with three bedrooms are one-third as many as the one-bedroom apartments, not equal to one-third of the total number of apartments.
2. There will be 70 one-bedroom apartments - To determine this, we need to calculate the number of two-bedroom and three-bedroom apartments first.
3. There will be 30 two-bedroom apartments - False, because one-third of the apartments have two bedrooms, which would be 70 (one-third of 210).
4. There will be 10 three-bedroom apartments - We need to use the relationship between the number of one-bedroom and three-bedroom apartments to determine this.

After doing the calculations:

• Two-bedroom apartments: 210 / 3 = 70
• One-bedroom apartments: There will be three times as many one-bedroom apartments as three-bedroom apartments.
• Let the number of three-bedroom apartments be x, then one-bedroom apartments will be 3x.
• Therefore, 70 (two-bedroom) + x (three-bedroom) + 3x (one-bedroom) = 210.
• Solving for x gives us x = 35, implying that there are 35 three-bedroom apartments.
• Since one-bedroom apartments are three times this, there will be 3 * 35 = 105 one-bedroom apartments.

The corrected statements would therefore be:

1. One-third of the apartments will have three bedrooms - False
2. There will be 70 one-bedroom apartments - False
3. There will be 30 two-bedroom apartments - False
4. There will be 10 three-bedroom apartments - False