Given:
A client is making a 10-lb bag of trail mix
The chocolates cost $4 per pound and mixed nuts cost $7 per pound
the client has a budget of $6.1 per pound
We will use the variables c and n to represent the number of pounds for chocolates and nuts
So, we have the following system of equations:
[tex]\begin{gathered} c+n=10\rightarrow(1) \\ 4c+7n=6.1\cdot10\rightarrow(2) \end{gathered}[/tex]
Solving the system by substitution method
From equation (1)
[tex]c=10-n\rightarrow(3)[/tex]
substitute with (c) from equation (3) into equation (2)
[tex]\begin{gathered} 4(10-n)+7n=6.1\cdot10 \\ \end{gathered}[/tex]
solve the equation to find (n)
[tex]\begin{gathered} 4\cdot10-4n+7n=6.1\cdot10 \\ -4n+7n=6.1\cdot10-4\cdot10 \\ 3n=21 \\ n=\frac{21}{3}=7 \end{gathered}[/tex]
Substitute with (n) into equation (3) to find (c)
[tex]c=10-7=3[/tex]
so, the answer will be:
The number of pounds of chocolates = c = 3 pounds
The number of pounds of nuts = n = 7 pounds
