Question

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.

Answer 1

5x + 2y = 50



x + 2y = 30

Answer 2

The system of equations is

`5x+2y=50`

`x+2y=30`

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

`5x+2y=50` -------> equation A

Prodution time needed for painting and assembling each doghouse

`x+2y=30` -------> equation B

Subtract equation B from equation A

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

`4x=20`

`x=5\ vinyl\ doghouses`

solve for y

`5+2y=30`

`2y=30-5`

`y=12.5\ treated\ lumber\ doghouses`