Let X = the number of pounds of $2.70 coffee and 
let Y = the number of pounds of $5.00 coffee.

When he mixes them together he will have X+Y pounds of coffee,
so we have the equation

X+Y = 100

If he could sell the X pounds of $2.75 coffee without mixing it, 
it would bring him in 2.75X dollars.

If he could sell the Y pounds of $5.00 coffee without mixing it, 
it would bring him in 5.00Y dollars.

So if he sold them both without mixing them they would bring him in
a total of 2.75X + 5.00Y dollars.

But if he mixed them together and sold them he would have 100 pounds 
of coffee selling for $3.90 per pound and that would bring him in 390
dollars.

So the other equation comes from setting the amount he would take in
if he could sell them separately equal to the amount he would take in
if he mixes them first.

 2.75X + 5.00Y = 390

So we have the system:



Solve that system of equations and get:

He would mix  pounds of the cheaper coffee and  pounds
of the more expensive coffee.

Edwin