Question

Formulate a system of equations for the situation below and solve. Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedrom townhes units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be 3 times the number of three-hedroom units. find how many units of each type will be in the complex.

Answer 1

The number of one-bedroom units is 3, the number of two-bedroom townhouses is 2, and the number of three-bedroom townhouses is 1 in the complex.

Step-by-step explanation:

Let's represent the number of one-bedroom units as x, the number of two-bedroom townhouses as y, and the number of three-bedroom townhouses as z.

According to the given information, the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. So, y + z = x.

Also, the number of one-bedroom units will be 3 times the number of three-bedroom units. So, x = 3z.

Combining these two equations, we have y + z = 3z.

To solve this system of equations, we can substitute the value of x from the second equation into the first equation:

y + z = 3z

y = 2z

Substituting y = 2z into the first equation:

2z + z = 3z

3z = 3z

z can be any real number. Let z = 1 for simplicity.

Therefore, the number of one-bedroom units (x) = 3z = 3.

The number of two-bedroom townhouses (y) = 2z = 2.

The number of three-bedroom townhouses (z) = 1.