An order of sunflower seeds and pumpkin seeds weighs 20 pounds and costs $13.

Question

Sunflower seeds: $0.75 per pound
Pumpkin seeds: $0.50 per pound
How many pounds of sunflower seeds and pumpkin seeds are in this order?
Start by writing an expression to represent the cost of s pounds of sunflower seeds. Keep in mind that 1 pound of sunflower seeds costs $0.75
Cost of s
pounds of
sunflower seeds
+
Cost of p pounds of pumpkin seeds
=
Total Cost
+
?
=
?
Great job!
Now, add an expression to represent the cost of p pounds of pumpkin seeds. Keep in mind that 1 pound of pumpkin seeds costs $0.50.
Cost of
s
pounds of sunflower seeds
+
Cost
of
p
pounds of
pumpkin seeds
=
Total Cost
0.75s
+
=
?
Great job!
Finally, what do you need to set the expression equal to? Reread the problem to determine the total cost of the order.
Cost of sunflower seeds
+
Cost of pumpkin seeds
=
Total
Cost
0.75s
+
0.5p
=

Answer 1

To solve the problem, let's define the variables:

• Let \( s \) be the number of pounds of sunflower seeds.
• Let \( p \) be the number of pounds of pumpkin seeds.

Step 1: Write expressions for costs

1. Cost of sunflower seeds: \[ \text{Cost of } s \text{ pounds of sunflower seeds} = 0.75s \]

2. Cost of pumpkin seeds: \[ \text{Cost of } p \text{ pounds of pumpkin seeds} = 0.50p \]

Step 2: Combine the cost expressions

Combining these expressions gives: \[ 0.75s + 0.50p = \text{Total Cost} \]

Step 3: Set the equation equal to the total cost

From the problem, we know the total cost of the order is $13. Hence, we write: \[ 0.75s + 0.50p = 13 \]

Step 4: Set up the additional equation for weight

We also know the total weight of the seeds is 20 pounds, which gives us the second equation: \[ s + p = 20 \]

Summary of equations

Now we have a system of equations:

1. \( 0.75s + 0.50p = 13 \)
2. \( s + p = 20 \)

Step 5: Solve the system of equations

To solve, we can express \( p \) in terms of \( s \) from the second equation: \[ p = 20 - s \]

Now substitute \( p \) in the first equation: \[ 0.75s + 0.50(20 - s) = 13 \]

Distributing the 0.50: \[ 0.75s + 10 - 0.50s = 13 \]

Combine like terms: \[ 0.25s + 10 = 13 \]

Subtract 10 from both sides: \[ 0.25s = 3 \]

Divide by 0.25: \[ s = 12 \]

Now substitute \( s \) back to find \( p \): \[ p = 20 - s = 20 - 12 = 8 \]

Final Answer

The order contains:

• 12 pounds of sunflower seeds
• 8 pounds of pumpkin seeds