Question

Universal Pet house sells vinyl doghouse and treated lumber doghouses. 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. 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.

Answer 1

5x + 2y = 50

x + 2y = 30

O believe that's the answer

Answer 2

The system of equations is :

Equation 1-
`5x+2y=50`

Equation 2-
`x+2y=30`

Number of vinyl doghouse = 5

Number of treated lumber doghouse =12.5

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-
`5x+2y=50`

→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-
`x+2y=30`

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

Subtract equation 2 from equation 1

`5x+2y-x-2y=50-30`

`4x=20`

`x=(20)/(4)`

`x=5`

Put value of x in equation 2

`x+2y=30`

`5+2y=30`

`2y=25`

`y=(25)/(2)`

`y=12.5`

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