Question 115263
Let x gallons of $15 paint and y gallons of $18 paint are mixed to get 12 gallons of $16.75 paint.

From this, we come to know, x + y = 12. 

Also, the rate of 12 gallons mixture paint = 12 * 16.75 = $201.

This should be equal to 15x + 18y.

So, we get 15x + 18y = 201 -----------(1)

We already have x + y = 12 -----------(2)

(2)* 15 gives,  15x + 15y = 180 -------(3)

(1) - (3) gives,    3y = 21.

This gives,    y = 7.

Plug in (2). We get, x = 5.

So, 5 gallons of $15 paint and 7 gallons of $18 paint gives a mixture of 12 gallons of $16.75 paint.