To solve: The problemby modeling and solving a system of linear equation. Th

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.
4) Solve the system as obtained in Step 3.
5) Check for the correctness of the solution by substituting back the values from Step 4 in the equations in Step 3 thereby verifying the statements in the given problem.
6) State the answer statement.
Calculation:
Step 1:
The given problem is a mixer problem where vanilla ice cream and peach ice cream are mixed together to make swirl ice cream where number of containers of each type is to be calculated.
Step 2:
There are two unknowns in the problem. Let number of containers of vanilla ice cream is v and that of peach ice cream is p.
Step 3:
The mixer problem is summarized in Table 1.
$\begin{array}{|ccc|}\hline Name& \text{Number of containers}& \text{Cost(Per container)}\\ \text{Vanilla ice cream}& v& \$6\\ \text{Peach ice cream}& p& \$11.50\\ \hline\end{array}$
Table 1
Total number of containers are 11. So, sum of containers of both types of ice cream should equal to 11.
${\displaystyle v+p=11}$
Total cost is $88. So, cost for vanilla ice cream and peach ice cream will be equal to $88.
${\displaystyle 6v+11.5p=88}$
Thus, the system of linear equations is:
${\displaystyle v+p=11\left(1\right)}$
${\displaystyle 6v+11.5p=88\left(2\right)}$
Step 4:
Substitute the value of p from equation (1) to (2).
${\displaystyle 6v+11.5(11-v)=88}$
${\displaystyle 6v+126.5-11.5v=88}$
${\displaystyle 5.5v=38.5}$
Solve the equation above to obtain the value of variable p as:
${\displaystyle 5.5v=38.5}$
${\displaystyle v=\frac{38.5}{5.5}}$
${\displaystyle v=7}$
Substitute the value of the variable p in equation (1) to obtain the value of the variable v as follows:
${\displaystyle \left(7\right)+p=11}$
${\displaystyle p=11-7}$
${\displaystyle p=4}$
Thus, the values of unknowns defined in Step 2 are ${\displaystyle v=7}$ and ${\displaystyle p=4}$.
Step 5:
To check the solution obtained in Step 4, the total containers are ${\displaystyle 7+4=11}$ and the total cost is ${\displaystyle 6\left(7\right)+11.5\left(4\right)=88}$.
Step 6:
Hence, the number of containers of vanilla ice cream is 7 and number of containers of peach ice cream is 4.