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

Question

Mathematics

Bridget Best

4 March, 22:33

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

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Answers (1)

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Wiggles · Answer 1

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