Since c represents the number of pounds of chocolates
Since n represents the number of pounds of nuts
Since Clint is making 10 pounds of them, then
[tex]c+n=10\rightarrow(1)[/tex]Since the cost of 1 pound of chocolates is $3.00
Since the cost of 1 pound of nuts is $6.00
Since the Clint budget is $5.1 per pound, then
[tex]10\times5.1-\text{ \$51}[/tex]Multiply c by 3 and n by 6, then add the products and equate the sum by 51
[tex]\begin{gathered} 3(c)+6(n)=5.1 \\ 3c+6n=51\rightarrow(2) \end{gathered}[/tex]The system of equations is
c + n = 10
3c + 6n = 51
Let us solve them
Multiply equation (1) by -3 to make the coefficient of c equal in values and different in signs
[tex]\begin{gathered} -3(c)-3(n)=-3(10) \\ -3c-3n=-30\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3)
[tex]\begin{gathered} (3c-3c)+(6n-3n)=(51-30) \\ 0+3n=21 \\ 3n=21 \end{gathered}[/tex]Divide both sides by 3 to find n
[tex]\begin{gathered} \frac{3n}{3}=\frac{21}{3} \\ n=7 \end{gathered}[/tex]Substitute n by 7 in equation (1)
[tex]c+7=10[/tex]Subtract 7 from both sides
[tex]\begin{gathered} c+7-7=10-7 \\ c=3 \end{gathered}[/tex]He should use 3 pounds of chocolate
He should use 7 pounds of nuts
If his budget is $51
