A company makes t-shirts and their research shows that that price and demand are related linearly: p = mx + b. They know that in order to sell 10 shirts they need to set the price at $26, and in order to sell 20 shirts they need to set the price at $6. Find the linear equation relating price to demand. p= c. Preview

Answer:The linear equation relating price to demand is [tex]p=-2x+46[/tex]Step-by-step explanation:Given : A company makes t-shirts and their research shows that that price and demand are related linearly :[tex]p=mx+b[/tex]. They know that in order to sell 10 shirts they need to set the price at $26, and in order to sell 20 shirts they need to set the price at $6.To Find : The linear equation relating price to demand ?Solution : A company makes t-shirts and their research shows that that price and demand are related linearly : [tex]p=mx+b[/tex]Where, p is the price and x is the demandIn order to sell 10 shirts they need to set the price at $26.i.e. p=26 and x=10The equation form is [tex]26=10m+b[/tex] ....(1)In order to sell 20 shirts they need to set the price at $6.i.e. p=6 and x=20The equation form is [tex]6=20m+b[/tex] ....(2)Solving (1) and (2) to get m and b,Subtract (1) from (2),[tex]6-26=20m+b-(10m+b)[/tex][tex]-20=20m+b-10m-b[/tex][tex]-20=10m[/tex][tex]m=-\frac{20}{10}[/tex][tex]m=-2[/tex]Substitute in equation (1), [tex]26=10(-2)+b[/tex] [tex]26+20=b[/tex] [tex]b=46[/tex]Substitute in the original relationship,[tex]p=mx+b[/tex][tex]p=(-2)x+46[/tex]Therefore, the linear equation relating price to demand is [tex]p=-2x+46[/tex]