Math Problem Statement
Solution
To solve this problem, we will set up a system of equations based on the information given:
Let:
- = the number of pounds of peanuts
- = the number of pounds of walnuts
The problem states:
-
The total weight of the mixture is 100 pounds:
-
The total cost of the mixture is calculated by the sum of the individual costs of peanuts and walnuts, which equals the cost of the entire mixture:
Simplifying the second equation:
Now, we solve this system of equations:
-
From the first equation:
-
Substitute in the second equation:
-
Simplify and solve for :
So, pounds of peanuts.
- Substitute into the first equation to find :
Thus, there are 60 pounds of peanuts and 40 pounds of walnuts in the mixture.
Summary
- Peanuts: 60 pounds
- Walnuts: 40 pounds
Would you like more details or have any questions?
Further Questions:
- How would the mixture's price change if the cost of walnuts increased?
- What happens if the total weight of the mixture changes?
- Can we calculate the percentage of peanuts and walnuts in the mixture?
- How would the mixture change if a third nut type was introduced?
- What is the effect of increasing the peanut cost to $2.00 per pound?
Tip: Always double-check each step in a system of equations to avoid calculation errors!
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Math Problem Analysis
Mathematical Concepts
Algebra
System of Equations
Linear Equations
Formulas
x + y = 100
1.41x + 2.61y = 189
Theorems
Linear combination of equations
Suitable Grade Level
Grades 7-10
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