simultaneous equations

Question

price of an item is ghc 3.50 when 250 items are demand, when only 50 are demanded the price rises to ghc 5.50 per item. identify the linear demand function and calculate the price per item at demand level of 115

Answer 1

p=mq+b where p=price, q=quantity, and m and b are constants, is the demand function.

3.50=250q+b, 5.50=50q+b. Subtract one equation from the other: 2=-200q so q=-1/100=-0.01.

3.50=-2.5+b and b=6. Therefore the demand function is p=6-0.01q.

When the demand level is 115, q=115 and p=6-1.15=ghc 4.85.