To solve: The problem by modeling and solving a system

Zoe Oneal

Zoe Oneal

Answered question


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

Answer & Explanation



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."
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.
NameAmount(in $)Cost(Per $)Peanutsp4Almondsa6.50
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 =5 pounds ×$5
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 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(3)+6.50(2)=25.
Step 6:
Hence, the number of pounds of peanuts is 3 and number of pounds of almonds is 2.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?