Price per unit and demand

Question

the price per unit, p, and the demand, x, for a particular material are related by the linear equation p=100-5/6x while the supply is given by the linear equation p=5/6x, at what value of p does supply equal demand

Answer 1

The value at which supply equals demand is when the two functions intersect. To calculate the intersection, set the two equations equal:

100 - 5/6x = 5/6x -- add 5/6x to both sides

100 = 10/6x -- multiply both sides by 6/10 -- the reciprocal of 10/6

100/1 * 6/10 = x -- simplify

600/10 = x

x = 60

Find p: 5/6 * 60/1 = 50

This means the supply will equal the demand when you set the price to $50 and sell 60 units.

Answer 2

Since p = 100 - (5/6)x and p = (5/6)x, we can equate these two values of p and solve for x:

100 - (5/6)x = (5/6)x

100 = (10/6)x

100 = (5/3)x

x = 100*(3/5)

x = 60

When the demand is 60, the value of p will be equal for supply and demand. Using our value of 60, we can substitute it in either of our p equations:

1) p = 100-(5/6)(60)

p = 50

2) p = (5/6)(60)

p = 50

Thus, the price per unit will be 50 when they are equal for supply and demand, for a given demand of 60.

Answer 3

100 - (5/6)x = (5/6)x

100 = (5/6)x + (5/6)x

100 = (10/6)x

100 = (5/3) x

100*3/5 = x

x = 60

at x=60, they are both 50