How many pounds of coffee worth $7 a pound should be added to 30 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound

Let's begin by assigning a letter to represent our unknown:
x = lbs. of coffee at $7 per lb.

Now let's write an equation to express the cost of mixing the $7 per lb. coffee with the $4 per lb. coffee based upon how many pounds we have of each:
(7)(x) + (4)(10) = (5)(x + 10)

Solving our equation for x:
7x + 40 = 5x + 50
7x - 5x = 50 - 40
2x = 10
x = 5 (lbs. of coffee at $7 per lb.)

We can verify our answer by plugging our answer back into our equation and checking to see that both sides balance:
(7)(x) + (4)(10) = 5(x + 10)
(7)(5) + 40 = 5(5 + 10)
35 + 40 = 25 + 50
75 = 75 (both sides balance)

Since both sides balance, we are confident that our answer is correct.
Hope this helps !