Question

The build a dream construction company has plans for two models of the homes they build, model a and model b. The model a home requires 18 single windows and 3 double windows. The model b home requires 20 single windows and 5 double windows. A total of 1,800 single windows and 375 double windows have been ordered for the developments. Write and solve a system of equations to represent this situation. Define your variables. Interpet the solution of the linear system in terms of the problem situation

Answer 1

Answer:

a = 50 houses

b = 45 houses

Step-by-step explanation:

Given

Number of houses called Model A = a

Number of houses called Model B = b

Total of single windows = 1800

Total of double windows = 375

then we have the system of equations

18a + 20b = 1800  (I)

3a + 5b = 375     (II)

Solving the system by whatever method we prefer, we obtain

(I)     a = (1800 - 20b)/18

then (II)

3((1800 - 20b)/18) + 5b = 375

⇒ 300 - (10/3)*b + 5b = 375

⇒ (5/3)*b  = 75

⇒ b = 45 houses

then

a = (1800 - 20*45)/18

⇒ a = 50 houses