Zoe Oneal

2021-08-13

To solve: The problem by modeling and solving a system of linear equations.

Mayme

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.
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.

Total amount of butter is 5 pounds, so sum of amount of both peanuts and almonds is 5 pounds.
$a+p=5$
The total cost is calculated as follows.
Total cost $=5$ pounds $×\mathrm{}5$
$=\mathrm{}25$
Total cost is $25. So, cost for almond and peanuts butter will be equal to$25.
$6.5a+4p=25$
Thus, the system of linear equations is:
$a+p=5\left(1\right)$
$6.5a+4p=25\left(2\right)$
Step 4:
Substitute the value of p from equation (1) to (2).
$6.5a+4p=25$
$6.5a+4\left(5-a\right)=25$
$6.5a+20-4a=25$
$2.5a=25-20$
Solve the equation above to obtain the value of variable p as:
$2.5a=5$
$a=\frac{5}{2.5}$
$a=2$
Substitute the value of the variable a in equation (1) to obtain the value of the variable p as follows:
$\left(2\right)+p=5$
$p=5-2$
$p=3$
Thus, the values of unknowns defined in Step 2 are $a=2$ and $p=3$.
Step 5:
To check the solution obtained in Step 4, the total pounds are $2+3=5$ and the total cost is $4\left(3\right)+6.50\left(2\right)=25$.
Step 6:
Hence, the number of pounds of peanuts is 3 and number of pounds of almonds is 2.

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