Question

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 1

Answer:

The linear equation relating price to demand is $p=-2x+46$

Step-by-step explanation:

Given : 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.

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 : $p=mx+b$

Where, p is the price and x is the demand

In order to sell 10 shirts they need to set the price at $26.

i.e. p=26 and x=10

The equation form is $26=10m+b$ ....(1)

In order to sell 20 shirts they need to set the price at $6.

i.e. p=6 and x=20

The equation form is $6=20m+b$ ....(2)

Solving (1) and (2) to get m and b,

Subtract (1) from (2),

$6-26=20m+b-(10m+b)$

$-20=20m+b-10m-b$

$-20=10m$

$m=-\frac{20}{10}$

$m=-2$

Substitute in equation (1),

$26=10(-2)+b$

$26+20=b$

$b=46$

Substitute in the original relationship,

$p=mx+b$

$p=(-2)x+46$

Therefore, the linear equation relating price to demand is $p=-2x+46$