Suppose that a certain product has the following demand and supply functions. demand: p = −0.05q + 45 supply: p = 0.05q + 10 if a $5 tax per item is levied on the supplier and this tax is passed on to the consumer, find the market equilibrium point after the tax.

(q, p) =

We can add 0.05q on both sides and we got:

Now we can subtract 15 on both sides and we got:

And then we can replace on any of the two functions to find the price like this:

Or equivalently

So then the equilibirum point is (q=300 units, p=30 $) for this case.

Step-by-step explanation:

For this case we have the following functions for the demand and the suppy:

Demand

Supply

For this case we have this condition: "If a $5 tax per item is levied on the supplier and this tax is passed on to the consumer", so then we need to add $5 to our supply function in order to satisfy this and our new equations are:

Demand

Supply

And the demand for this case not change since the taxes are just related to the supply function. And now we just need to set equal the equations for the demand and supply and solve for the equilibrium point:

We can add 0.05q on both sides and we got:

Now we can subtract 15 on both sides and we got:

And then we can replace on any of the two functions to find the price like this:

Or equivalently

So then the equilibirum point is (q=300 units, p=30 $) for this case.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

well there are two answers for that.

1: you need 120 ones then that will equal up to 120.

2: you could also do one 100 and 2 tens.

those are the answers that i have thought of.