Answer:
The system of equations is :
Equation 1- [tex]5x+2y=50[/tex]
Equation 2- [tex]x+2y=30[/tex]
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- [tex]5x+2y=50[/tex]
→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- [tex]x+2y=30[/tex]
→When we solve these equation we get the number of vinyl doghouse and treated lumber doghouse.
Subtract equation 2 from equation 1
[tex]5x+2y-x-2y=50-30[/tex]
[tex]4x=20[/tex]
[tex]x=\frac{20}{4}[/tex]
[tex]x=5[/tex]
Put value of x in equation 2
[tex]x+2y=30[/tex]
[tex]5+2y=30[/tex]
[tex]2y=25[/tex]
[tex]y=\frac{25}{2}[/tex]
[tex]y=12.5[/tex]
Therefore, number of vinyl doghouse = 5, number of treated lumber doghouse =12.5
