Nuts worth$.90 per pound are to be mixed in nuts worth $1.60 per pound to make 175 pounds of mixture worth $1.30 per pound. How much of each used?

Question

I have done so many of these but for some reason I cant figure a couple out, please help.

Answer 1

Hi Caleb,

Let's begin by assigning a letter for 1st unknown:
    x (# of lbs. at $0.90 per lb.)

Next, we'll write an expression for 2nd unknown in terms of 1st unknown:
   175 - x (# of lbs. at $1.60 per lb.)

Now we'll write an equation to express the total cost of the mixture in terms of the price and number of pounds of each component:
    (0.90)(x) + (1.60)(175 - x) = (1.30)(175)

Now we'll solve our equation for our 1st unknown (x):

    (0.90)(x) + (1.60)(175 - x) = (1.30)(175)

     0.90x + 280 - 1.60 = 227.50

     -0.70x + 280 = 227.50

     -0.70x = 227.50 - 280

     -0.70x = -52.50

            x = -52.50/-0.70

            x = 75 (# of lbs. at $0.90 per lb.)

 

Next, we'll determine our 2nd unknown based upon our expression using the value of our 1st unknown:

      175 - x = 75

             -x  = 75 - 175

             -x = -100

      (-1)(-x) = (-1)(-100)

              x = 100 (#of lbs. at $1.60 per lb.)

We can verify that our answers are correct by plugging in our values for the number of pounds of each component into our total cost equation and see if the sum of the component costs equals given total cost of the mixture:

     (0.90)(x) + (1.60)(175 - x) = (1.30)(175)
     (0.90)(75) + (1.60)(100) = 227.50

     67.50 + 160.00 = 227.50
     227.50 = 227.50 (answers are correct)

Once we were able to express one unknown in terms of the other unknown, we were able to come up with the right equation to get our answers.

Thanks for submitting this problem and glad to help.

God bless, Jordan.