Cantwell associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units, two-bedroom townhouses, and three-bedroom townhouses. a total of 216 units is planned. the total number of 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-bedroom townhouses, find how many units of each type will be in the complex. one-bedroom units units two-bedroom townhouses units three-bedroom townhouses units

108 one-bedroom units

72 two-bedroom units

36 three-bedroom units

Step-by-step explanation:

Let x, y, z the number of one-bedroom, two-bedroom and three-bedroom units respectively. Then  

1) x+y+z = 216

2)     y+z = x

3)         x = 3z

Multiplying equation 1) by -1 and adding it to 2), we get

-x = x-216 so, x = 216/2 = 108

x = 108

Replacing this value in 3) we get

z = 108/3 = 36

z = 36

Replacing now in 2)

y+36 = 108, y = 108-36 and

y = 72

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240