Question

The price-demand equation for gasoline is 0.3d + 4p = 80, where p is the price per gallon in dollars and d is the daily demand measured in millions of gallons. Write the demand d as a function of price What is the demand if the price is $ 8 per gallon?

Answer 1

Answer:

The demand d as a function of price is $d=\frac{800}{3} -\frac{40p}{3}$

The demand if the price is $ 8 per gallon is 160 millions of gallons.

Step-by-step explanation:

You know that the price-demand equation for gasoline is 0.3d + 4p = 80

To write demand d as a function of price p, you must solve for or isolate demand d, remembering that:

• All the terms that are multiplying on one side, go to the other side of the equality by dividing, and those that are dividing go to the other side of the equality by multiplying.

• The terms that are adding go to the other side of the equality by subtracting and those that are subtracting go to the other side by adding.

So:

0.3d + 4p = 80

0.3d = 80 - 4p

$d=\frac{80 - 4p}{0.3}$

$d=\frac{80}{0.3} -\frac{4p}{0.3}$

$d=\frac{800}{3} -\frac{40p}{3}$

The demand d as a function of price is $d=\frac{800}{3} -\frac{40p}{3}$

To determine how much is the quantity demanded if the price is $ 8 per gallon, you simply plug that value into the previously determined expression and perform the corresponding calculations:

$d=\frac{800}{3} -\frac{40*8}{3}$

$d=\frac{800}{3} -\frac{320}{3}$

d= 160

The demand if the price is $ 8 per gallon is 160 millions of gallons.