Let's call X the number of pounds of cashews and Y the number of pounds of Brazil nuts.
Now, we want to make 33 pounds of the mixture, so:
X + Y = 33
Adittionally, every pound mixture will be sell for $5.64 per pound. It means that:
7X + 4Y = 5.64*33
7X + 4Y = 186.12
Because every pound of cashews cost $7 and every pound of Brazil nuts cost $4
Then, we can solve for X on the first equation and replace it on the second as:
[tex]\begin{gathered} X+Y=33 \\ X=33-Y \end{gathered}[/tex][tex]\begin{gathered} 7X+4Y=186.12 \\ 7(33-Y)+4Y=186.12 \end{gathered}[/tex]So, we can solve for Y as:
[tex]\begin{gathered} 7\cdot33-7\cdot Y+4Y=186.12 \\ 231-7Y+4Y=186.12 \\ 231-3Y=186.12 \\ -3Y=186.12-231 \\ -3Y=-44.88 \\ Y=\frac{-44.88}{-3} \\ Y=14.96 \end{gathered}[/tex]Now, we can calculate X as:
[tex]\begin{gathered} X=33-Y \\ X=33-14.96 \\ X=18.04 \end{gathered}[/tex]Therefore, we need to use 18.04 pounds of cashews and 14.96 pounds of Brazil nuts to make a 33 pounds mixture that sells for $5.64 per pound
Answer 18.04 pounds of cashews and 14.96 pounds of Brazil nuts
