To solve: The problem by modeling and solving a system

Procedure used:
"Model and solve system of linear equations
1) Identify the category of given problem.
2) Recognize and algebraically name the unknowns.
3) Translate the problem statement as a system of linear equations using the variables from Step 2.
S 4) Solve the system as obtained in Step 3.
5) State the answer statemen."
Calculation:
Step 1:
The given problem is a mixer problem where peanuts and almonds are mixed together to make almond-peanut butter where number of pounds of each type is to be calculated.
Step 2:
There are two unknowns in the problem. Let total amount of almonds is a and that of peanuts is p.
Step 3:
The mixer problem is summarized is Table.
$\begin{array}{|ccc|}\hline Name& Amount(in\$)& Cost(Per\$)\\ Peanuts& p& 4\\ Almonds& a& 6.50\\ \hline\end{array}$
Total amount of butter is 5 pounds, so sum of amount of both peanuts and almonds is 5 pounds.
${\displaystyle a+p=5}$
The total cost is calculated as follows.
Total cost ${\displaystyle =5}$ pounds ${\displaystyle \times \mathrm{\$}5}$
${\displaystyle =\mathrm{\$}25}$
Total cost is $25. So, cost for almond and peanuts butter will be equal to $25.
${\displaystyle 6.5a+4p=25}$
Thus, the system of linear equations is:
${\displaystyle a+p=5\left(1\right)}$
${\displaystyle 6.5a+4p=25\left(2\right)}$
Step 4:
Substitute the value of p from equation (1) to (2).
${\displaystyle 6.5a+4p=25}$
${\displaystyle 6.5a+4(5-a)=25}$
${\displaystyle 6.5a+20-4a=25}$
${\displaystyle 2.5a=25-20}$
Solve the equation above to obtain the value of variable p as:
${\displaystyle 2.5a=5}$
${\displaystyle a=\frac{5}{2.5}}$
${\displaystyle a=2}$
Substitute the value of the variable a in equation (1) to obtain the value of the variable p as follows:
${\displaystyle \left(2\right)+p=5}$
${\displaystyle p=5-2}$
${\displaystyle p=3}$
Thus, the values of unknowns defined in Step 2 are ${\displaystyle a=2}$ and ${\displaystyle p=3}$.
Step 5:
To check the solution obtained in Step 4, the total pounds are ${\displaystyle 2+3=5}$ and the total cost is ${\displaystyle 4\left(3\right)+6.50\left(2\right)=25}$.
Step 6:
Hence, the number of pounds of peanuts is 3 and number of pounds of almonds is 2.