Can someone help with this question pls

Question

The nut shack sells hazelnuts for $6.50 per pound and peanuts nuts for $5.20 per pound. How much of each type should be used to make a 38 pound mixture that sells for $5.82 per pound?

Answer 1

Let: 

X=hazelnuts

Y=peanuts

 We have 2 unknowns, therefore we need 2 equations to solve the problem. We know that our total pounds is 38 and $5.82 per pound. Therefore:

    X + Y = 38 pounds

    6.50X + 5.20Y = 5.82

By using the substitution method:

    Y = 38 - X (from the first equation)

Substituting this value of X into the 2nd equation we can solve for Y:

    6.50X + 5.20(38-X) = 5.82(38)

    6.50X + 197.6-5.20X= 221.16

    1.3X = 23.56

    X = 23.56/1.3

     X=18.12

Putting this value of X into the 1st equation we can solve for Y:

     Y= 38 - X

     Y = 38 -(18.12)

     Y =19.88

Therefore the answer is:

     18.12 pounds of hazelnut and 19.88 pounds of peanuts to get a mixture that will sell for $5.82 per pound