We have to find how many pounds of each mix we have to use in the new mix.
Let A be the pounds for the first mix, which is sold at $1.20 per pound.
Let B be the pounds for the second mix, which is sold at $2.35 per pound.
We then can use the information given to write a system of equations and solve for A and B.
We know that the total weight is 24 pounds, so we can write:
[tex]A+B=24[/tex]The price per pound for the mix is $1.65, so the total mix has to be sold at 24*1.65 = $39.60.
This price for the mix will be equal to the sum of the weight of each mix times its price per pound.
Then, we can write:
[tex]\begin{gathered} 1.20\cdot A+2.35\cdot B=1.65\cdot24 \\ 1.2A+2.35B=39.6 \end{gathered}[/tex]We can use the first equation to express A in function B:
[tex]\begin{gathered} A+B=24 \\ A=24-B \end{gathered}[/tex]Then, we replace A in the second equation and solve for B as:
[tex]\begin{gathered} 1.2A+2.35B=39.6 \\ 1.2(24-B)+2.35B=39.6 \\ 28.8-1.2B+2.35B=39.6 \\ 2.35B-1.2B=39.6-28.8 \\ 1.15B=10.8 \\ B=\frac{10.8}{1.15} \\ B\approx9.39 \end{gathered}[/tex]Knowing B = 9.39 we can calculate A as:
[tex]\begin{gathered} A=24-B \\ A=24-9.39 \\ A=14.61 \end{gathered}[/tex]Answer:
14.61 pounds of the $1.20 mix.
9.39 pounds of the $2.35 mix.
