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

Answer:

The system of equations is

$5x+2y=50$

$x+2y=30$

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

$5x+2y=50$ -------> 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

$5+2y=30$

$2y=30-5$

$y=12.5\ treated\ lumber\ doghouses$