Question

An order of cashews and peanuts weighs 11 pounds and costs $31.
Cashews: $3.00 per pound
Peanuts: $2.50 per pound
How many pounds of cashews and peanuts are in this order?
Start by writing an expression to represent the cost of c pounds of cashews. Keep in mind that 1 pound of cashews costs $3.00
Cost of c
pounds of
cashews
+
Cost of p pounds of peanuts
=
Total Cost
+
?
=
?

Answer 1

To solve this problem, we need to find the number of pounds of cashews (c) and peanuts (p) in the order. We have the following information:

1. The total weight of the order is 11 pounds:
\[
c + p = 11
\]

2. The total cost of the order is $31. Since cashews cost $3.00 per pound and peanuts cost $2.50 per pound, the cost can be expressed as:
\[
3c + 2.5p = 31
\]

We can now summarize the situation with these two equations:

1. \( c + p = 11 \) (Equation 1)
2. \( 3c + 2.5p = 31 \) (Equation 2)

### Step 1: Express p in terms of c
From Equation 1:
\[
p = 11 - c
\]

### Step 2: Substitute p in Equation 2
Now we can substitute \( p \) in Equation 2:
\[
3c + 2.5(11 - c) = 31
\]

### Step 3: Expand and simplify
Expanding the equation:
\[
3c + 27.5 - 2.5c = 31
\]
Combine like terms:
\[
(3c - 2.5c) + 27.5 = 31
\]
\[
0.5c + 27.5 = 31
\]

### Step 4: Solve for c
Subtract 27.5 from both sides:
\[
0.5c = 31 - 27.5
\]
\[
0.5c = 3.5
\]

Multiply both sides by 2 to solve for \( c \):
\[
c = 7
\]

### Step 5: Solve for p
Now substitute back to find \( p \):
\[
p = 11 - c = 11 - 7 = 4
\]

### Summary of results
The order consists of:
- **7 pounds of cashews**
- **4 pounds of peanuts**

To verify:
- Weight check: \( 7 + 4 = 11 \) pounds (correct)
- Cost check: \( 3(7) + 2.5(4) = 21 + 10 = 31 \) dollars (correct)

Thus, the solution is:
\[
\text{Cashews: 7 pounds, Peanuts: 4 pounds}
\]