Dee wants to mix coffee worth $7 pound with coffee worth $4 a pound to get a mixture of 14 pounds $5 a pound . how many pounds of each must be mixed together to get the new blend?

so.. whatever "x" and "y" amounts are, we know that, added together, they must yield 14lbs
thus   x + y = 14

and whatever the cost of each is, 7x + 4y must be 14*5

7x+4y = 70
thus      

solve for "x", to see how much of the $7/lb type will be needed

what about the $4/lb one?   well, y = 14 - x