Randall wants to mix 44 lb of nuts worth $1 per lb with some nuts worth $9 per lb to make a mixture worth $8 per lb. How many pounds of $9 nuts must he use?

38.5 pounds

Step-by-step explanation:

Let pounds of $1 nuts used be "x"

Let pounds of $9 nuts used be "y"

44 lb of nuts in total, so we can say:

x + y = 44

or

x = 44 - y

Now, the mixture of 44 lb nuts would be worth $8, so we can write:

1x + 9y = 8 (44)

x + 9y = 352

We replace this with the 1st equation (x = 44 - y) and find the value of "y":

x + 9y = 352

44 - y + 9y = 352

8y = 352 - 44

8y = 308

y = 308/8

y = 38.5

So, we need to mix 38.5 pounds of $9 nuts