Answer :
Answer:
He should use 20.08 pounds of the $1.85 per pound kind of nuts in the new mix
He should use 8.92 pounds of $1.20 per pound kind of nuts in the new mix
Explanation:
Let x represent the pounds of $1.20 nut in the mix
Let y represent the pounds of $1.85 nut in the mix
So if he wants to mix a total of 29 pounds, we can set up the below equation;
[tex]x+y=29\ldots\ldots\text{.}\mathrm{}\text{Equation 1}[/tex]If he wants to sell it for $1.65 per pound, we can set up the below equation;
[tex]\begin{gathered} 1.2x+1.85y=1.65\times29 \\ 1.2x+1.85y=47.85,\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \end{gathered}[/tex]We can now solve the system of equations simultaneously following the below steps;
Step 1: Express x in terms of y in Equation 1;
[tex]x=29-y\ldots\ldots\ldots\text{.Equation 3}[/tex]Step 2: Substitute x with (29 - y) in Equation 2 and solve for y;
[tex]\begin{gathered} 1.2(29-y)+1.85y=47.85 \\ 34.8-1.2y+1.85y=47.85 \\ 34.8+0.65y=47.85 \\ 0.65y=47.85-34.8 \\ 0.65y=13.05 \\ \frac{0.65y}{0.65}=\frac{13.05}{0.65} \\ y=20.08\text{ pounds} \end{gathered}[/tex]So he should use 20.08 pounds of the $1.85 per pound kind of nuts in the new mix
Step 3: Substitute y with 20.08 in Equation 3 and solve for x;
[tex]x=29-20.8=8.92\text{ pounds}[/tex]So he should use 8.92 pounds of $1.20 per pound kind of nuts in the new mix
