Zoe Oneal

2021-08-13

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

Mayme

Skilled2021-08-14Added 103 answers

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.

Total amount of butter is 5 pounds, so sum of amount of both peanuts and almonds is 5 pounds.

The total cost is calculated as follows.

Total cost

Total cost is $25. So, cost for almond and peanuts butter will be equal to $25.

Thus, the system of linear equations is:

Step 4:

Substitute the value of p from equation (1) to (2).

Solve the equation above to obtain the value of variable p as:

Substitute the value of the variable a in equation (1) to obtain the value of the variable p as follows:

Thus, the values of unknowns defined in Step 2 are

Step 5:

To check the solution obtained in Step 4, the total pounds are

Step 6:

Hence, the number of pounds of peanuts is 3 and number of pounds of almonds is 2.

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