We will call the amount of each candy as X and Y.
Candy X sells for $1.20 per pound.
Candy Y sells for $2.00 per pound.
The total mix weights 26 pounds, so we can write:
[tex]X+Y=26[/tex]Then, the final price of the mix will be 26 pounds * 1.65 $/pound = $42.9. This final price is equal to the sum of X by its price and Y by its price:
[tex]\begin{gathered} 1.20\cdot X+2.00\cdot Y=1.65\cdot26 \\ 1.20X+2.00Y=42.9 \end{gathered}[/tex]Now we have a system of equations with two unknowns.
We can replace X in the second equation knowing that:
[tex]X=26-Y[/tex][tex]\begin{gathered} 1.20\cdot(26-Y)+2Y=42.9 \\ 31.2-1.2Y+2Y=42.9 \\ -1.2Y+2Y=42.9-31.2 \\ 0.8Y=11.7 \\ Y=\frac{11.7}{0.8} \\ Y=14.625 \end{gathered}[/tex]With the value of Y, we can calculate X as:
[tex]X=26-Y=26-14.625=11.375[/tex]Answer:
The amount of the $1.20 candy is 11.38 pounds and the amount of the $2 candy is 14.62 pounds.
