The plans for an apartment complex provided for 440 apartments, with each apartment having one, two, or three bedrooms. There were to be 30 more three-bedroom than one-bedroom apartments, and the number of two-bedroom apartments was to be 10 less than 3 times the number of one-bedroom apartments. How many apartments of each type were in the plans?
A) 84 one-bedrooms, 242 two-bedrooms, and 117 three-bedrooms
B) 84 one-bedrooms, 245 two-bedrooms, and 113 three-bedrooms
C) 84 one-bedrooms, 242 two-bedrooms, and 114 three-bedrooms
D) 114 one-bedrooms, 252 two-bedrooms, and 114 three-bedrooms
E) 114 one-bedrooms, 242 two-bedrooms, and 144 three-bedrooms

Question

Quizplus · Accepted Answer

Let's represent the number of one-bedroom apartments as x.

According to the problem:
- The number of three-bedroom apartments is 30 more than the number of one-bedroom apartments. So, the number of three-bedroom apartments is x+30.
- The number of two-bedroom apartments is 10 less than 3 times the number of one-bedroom apartments. So, the number of two-bedroom apartments is 3x-10.

We know that the total number of apartments is 440. So:

x + (x+30) + (3x-10) = 440
5x + 20 = 440
5x = 420
x = 84

So, there are 84 one-bedroom apartments in the plans.

Using the values we found before, we can find the number of two-bedroom and three-bedroom apartments:

Number of two-bedroom apartments = 3x-10 = 3(84)-10 = 242
Number of three-bedroom apartments = x+30 = 84+30 = 114

Therefore, there are 84 one-bedrooms, 242 two-bedrooms, and 114 three-bedrooms in the plans. The correct answer choice is C.

The Plans for an Apartment Complex Provided for 440 Apartments