Question

The Nut Shack sells hazelnuts for $7.50 per pound and peanuts nuts for $4.60 per pound. How much of eachtype should be used to make a 34 pound mixture that sells for $6.39 per pound

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

hazelnuts = $7.50 / lb

peanuts nuts = $4.60 / lb

total mixture (mass) = 34 lb

total mixture (price) = $6.39 / lb

Step 02:

system of equations:

x = pounds of hazelnuts

y = pounds of peanuts

x + y = 34 eq.1

7.50x + 4.60y = 6.39*34 eq.2

x, eq.1:

x = 34 - y

x in eq.2:

7.50(34 - y) + 4.60y = 6.39*34

255 - 7.5y + 4.6y = 217.26

-7.5 y + 4.6y = 217.26 - 255

-2.9y = -37.74

y = (-37.74) / (-2.9)

y = 13.01

y, eq.1 :

x + 13.01 = 34

x = 34 - 13.01 = 20.99

The answer is:

x = 21 pounds of hazelnuts

y = 13 pounds of peanuts