An order of cashews and peanuts weighs 11 pounds and costs $31.

Question

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: \[ \text{Cashews: 7 pounds, Peanuts: 4 pounds} \]