Question

The nutty professor sells cashews for $7.80 per pound and Brazil nuts for $4.10 per pound. How much of each type should be used to make a 34 pound mixture that sells for $5.73 per pound?

Answer 1

To make a 34 pound mixture that sells for $5.73 per pound, the nutty professor should use approximately 19.67 pounds of cashews and 14.33 pounds of Brazil nuts.

Step-by-step explanation:

To solve this problem, we can set up a system of linear equations. Let's represent the amount of cashews and Brazil nuts used as variables, with x representing cashews and y representing Brazil nuts. The total weight of the mixture is 34 pounds, so we have the equation:

x + y = 34

The cost of the mixture is $5.73 per pound, so we can set up another equation using the prices of the nuts:

7.80x + 4.10y = 5.73(34)

Simplifying the second equation gives us:

7.80x + 4.10y = 194.82

We can solve this system of equations using substitution or elimination. Let's use elimination by multiplying the first equation by 7.80 and subtracting it from the second equation:

7.80x + 4.10y = 194.82

(7.80x + 7.80y) - (7.80x + 4.10y) = (194.82) - (7.80(34))

3.70y = 53.01

Dividing both sides of the equation by 3.70 gives us:

y = 14.33

Substituting this value of y into the first equation, we can solve for x:

x + 14.33 = 34

x = 19.67

So, the nutty professor should use approximately 19.67 pounds of cashews and 14.33 pounds of Brazil nuts to make the 34 pound mixture.