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To solve this problem, we will set up a system of equations based on the information given:

Let:
- $ x $ = the number of pounds of peanuts
- $ y $ = the number of pounds of walnuts

The problem states:
1. The total weight of the mixture is 100 pounds: 
   \[
   x + y = 100
   \]

2. 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:
   \[
   1.41x + 2.61y = 1.89 \times 100
   \]

Simplifying the second equation:
\[
1.41x + 2.61y = 189
\]

Now, we solve this system of equations:

1. From the first equation: 
   \[
   y = 100 - x
   \]

2. Substitute $ y $ in the second equation:
   \[
   1.41x + 2.61(100 - x) = 189
   \]

3. Simplify and solve for $ x $:
   \[
   1.41x + 261 - 2.61x = 189
   \]
   \[
   -1.2x + 261 = 189
   \]
   \[
   -1.2x = 189 - 261
   \]
   \[
   -1.2x = -72
   \]
   \[
   x = 60
   \]

So, $ x = 60 $ pounds of peanuts.

4. Substitute $ x = 60 $ into the first equation to find $ y $:
   \[
   y = 100 - 60 = 40
   \]

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:
1. How would the mixture's price change if the cost of walnuts increased?
2. What happens if the total weight of the mixture changes?
3. Can we calculate the percentage of peanuts and walnuts in the mixture?
4. How would the mixture change if a third nut type was introduced?
5. 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!

A grocer mixes peanuts that cost $1.41 per pound and walnuts that cost $2.61 per pound to make 100 pounds of a mixture that costs $1.89 per pound. How much (in lb) of each kind of nut is in the mixture?

Solve the mixture problem where a grocer combines peanuts costing $1.41 per pound and walnuts costing $2.61 per pound to form 100 pounds of a mixture costing $1.89 per pound. Learn how to solve this system of linear equations step-by-step.

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