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

Answer:

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

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- $5x+2y=50$

→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

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

$4x=20$

$x=\frac{20}{4}$

$x=5$

Put value of x in equation 2

$x+2y=30$

$5+2y=30$

$2y=25$

$y=\frac{25}{2}$

$y=12.5$

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