The key to this type of problem is to find a system of equations that represent the problem. After that, it is as simple as substituting and simplifying.
Start by writing down the important information provided by the problem,
Cashews = $6.30 per pound
Brazil Nuts = $4.10 per pound
Mixture = $4.86 per pound
Note: We want to make a 29 pound mixture
Now we set up two equations using this information,
(Pounds of Cashews)(Cost of Cashews) + (Pounds of Brazil Nuts)(Cost of Brazil Nuts) = (Pounds of Mixture)(Cost of Mixture)
Let x = Pounds of Cashews
y = Pounds of Brazil Nuts
Then the final mixture will satisfy the following two equations
1) x + y = 29
2) x(6.30) + y(4.10) = 29(4.86)
Solve the first question for x,
x = 29 - y
Substitute this value into the second equation,
(29 - y)(6.30) + y(4.10) = 29(4.86)
Simplify and combine like terms,
-2.2y = -41.76
y ≈ 18.98
We can use this value of y in the first equation to find x,
x + y = 29
x + 18.98 = 29
x ≈ 10.02
The problem likely intends for you to round these answers.
Therefore, we should use 10 pounds of Cashews and 19 Pounds of Brazil Nuts to create the Mixture that sells for $4.86 per pound.
We can check this answer by plugging in these values to the second equation.
