The Nutty Professor sells cashews for $\$ 7.60$ per pound and Brazil nuts for $\$ 4.60$ per pound. How much of each type should be used to make a 32 pound mixture that sells for $\$ 6.01$ per pound? Round answers to the nearest pound. pounds of cashews pounds of Brazil nuts Question Help: $\square$ Video $1 \square$ Video $2 \square$ Video $3 \square$ Video $4 \square$ Video 5 Calculator Submit Question

Step 1 ：Let's denote the amount of cashews as \(x\) (in pounds) and the amount of Brazil nuts as \(y\) (in pounds).

Step 2 ：From the problem, we have two equations: \(x + y = 32\) and \(7.60x + 4.60y = 6.01 \times 32\).

Step 3 ：First, let's multiply the first equation by 4.60 to make the coefficients of \(y\) in both equations the same: \(4.60x + 4.60y = 4.60 \times 32\).

Step 4 ：Now, subtract this new equation from the second one: \(7.60x - 4.60x = 6.01 \times 32 - 4.60 \times 32\).

Step 5 ：This simplifies to: \(3x = 1.41 \times 32\).

Step 6 ：Divide both sides by 3 to solve for \(x\): \(x = 1.41 \times 32 / 3 \approx 15\) pounds (rounded to the nearest pound).

Step 7 ：Substitute \(x = 15\) into the first equation to solve for \(y\): \(15 + y = 32\).

Step 8 ：Solving for \(y\) gives: \(y = 32 - 15 = 17\) pounds.

Step 9 ：So, the Nutty Professor should use approximately \(\boxed{15}\) pounds of cashews and \(\boxed{17}\) pounds of Brazil nuts.