# Universal pet house sells vinyl doghouses and treated lumber doghouses. it takes the company 5 hours to build a vinyl doghouse and

Universal pet house sells vinyl doghouses and treated lumber doghouses. it takes the company 5 hours to build a vinyl doghouse and 2 hours to build a treated lumber doghouse. the company dedicates 50 hours every week towards building doghouses. it takes an additional hour to paint each vinyl doghouse and an additional 2 hours to assemble each lumber doghouse. the company dedicates 30 hours every week towards assembling and painting doghouses. write a system of equations that represent the production time needed to build each doghouse and the prodution time needed for painting and assembling each doghouse. use x to represent the number of vinyl doghouses and y to represent the number of treated lumber doghouses.

5x + 2y = 50

x + 2y = 30

The system of equations is

Step-by-step explanation:

Let

x------> the number of vinyl doghouses

y----->  the number of treated lumber doghouses

we know that

Production time needed to build each doghouse

-------> equation A

Prodution time needed for painting and assembling each doghouse

-------> equation B

Subtract equation B from equation A

solve for y

5x + 2y = 50

x + 2y = 30

build time= 5x+2y+50

paint/assembly time= x+2y=30

Step-by-step explanation:

The system of equations is :

Equation 1-

Equation 2-

Number of vinyl doghouse = 5

Number of treated lumber doghouse =12.5

Step-by-step explanation:

Let x be the number of vinyl doghouses

y be the number of treated lumber doghouses

→If it takes the company 5 hours to build a vinyl doghouses and 2 hours to build a treated lumber doghouse. The company dedicates 50 hours every week towards assembling and painting doghouses.

Equation 1-

→It takes an additional hour to paint each vinyl doghouse and an additional 2 hours to assemble each treated lumber doghouse. The company dedicates 30 hours every week towards assembling and paining dog houses.

Equation 2-

→When we solve these equation we get the number of  vinyl doghouse and treated lumber doghouse.

Subtract equation 2 from equation 1

Put value of x in equation 2

Therefore, number of vinyl doghouse = 5, number of treated lumber doghouse =12.5

Given:

5 hours to build 1 vinyl doghouse
2 hours to build 1 lumber doghouse
1 hour to paint 1 vinyl doghouse
2 hours to assemble 1 lumber doghouse

Company hours = 50 hours/week
For assembly and painting = 30 hours/week

Let x = number of vinyl dog houses
y = number of lumber dog houses

Build time = 5x
Build time = 2y
Paint time = x
Assembly time = 2y

Total time = 6x
= 4y

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