at a local grocery store the demand for ground beef is approximately 50 pounds per week when the price per pound is $4, but is only 40 pounds per week when the price rises to $5.50 per pound.

Question

1. at a local grocery store the demand for ground beef is approximately 50 pounds per week when the price per pound is $4, but is only 40 pounds per week when the price rises to $5.50 per pound.
2. a) Assuming a linear relationship between the demand x and the price per pound p, express the price as a function of demand.
3. b) Use this model to predict the demand if the price rises to $5.80 per pound.

Answer 1

the solution should be slightly less than 40 pounds. Maybe about 38 pounds

as price rises, the amount purchased decreases. It's a downward sloping demand curve, Price on the y axis, pounds,x, on the x axis.

It's a slight price increase of 30 cents, so there should be a slight decrease in quantity purchased.

price rose $1.50 and quantity decreased by 10 pounds. 30 is 1/5 of 150

30/150 = 3/15 = 1/5 or

3/15 times 10 = 2 pound decrease.

40- 2 =38 pounds bought at $5.80

(4, 50), (5.5,40) are two points on a line with slope = "rise over run" = (5.5-4)(40-50)= 1.4/-10= (P-4)/(x-50)

P-4 = (-3/20)(x-50) = -3x/20+ 15/2

P=-3x/20+23/2

20P= -3x+ 230

3x =230-20P

x = 230/3 - 20P/3

x =230/3 -20(5.8)/3

x = (230 - 116)/3 = 114/3 = 38 pounds bought at $5.80

("trivial point": don't say "demand" when you mean "quantity demanded" It sounds like hair splitting. It is if this is a problem in a math course. But if you're taking an economics course, you get points off for confusing them. "demand" is the demand curve, which doesn't change with a change in price. "quantity demanded" is a movement along the demand curve, and it changes as price changes)