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
+
?
=
?

Answer 1

Let's define our variables and write the necessary expressions:

Let:

• \( s \) = pounds of sunflower seeds
• \( p \) = pounds of pumpkin seeds

From the problem, we have two main equations:

1. The total weight equation: \[ s + p = 20 \]

2. The total cost equation: The cost of sunflower seeds is $0.75 per pound, so the cost for \( s \) pounds of sunflower seeds is: \[ 0.75s \]

   The cost of pumpkin seeds is $0.50 per pound, so the cost for \( p \) pounds of pumpkin seeds is: \[ 0.50p \]

   The total cost equation can be written as: \[ 0.75s + 0.50p = 13 \]

So, we have the following system of equations:

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

Now, let's use these equations to solve for \( s \) and \( p \).

From the first equation, we can express \( p \) in terms of \( s \): \[ p = 20 - s \]

Now we can substitute this expression for \( p \) into the second equation: \[ 0.75s + 0.50(20 - s) = 13 \]

Expanding this gives: \[ 0.75s + 10 - 0.50s = 13 \]

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

Now, isolate \( s \) by subtracting 10 from both sides: \[ 0.25s = 3 \]

Dividing by 0.25: \[ s = \frac{3}{0.25} = 12 \]

Now, we can find \( p \): \[ p = 20 - s = 20 - 12 = 8 \]

Thus, the solution is:

• Sunflower seeds: \( s = 12 \) pounds
• Pumpkin seeds: \( p = 8 \) pounds

To summarize:

• Sunflower seeds: 12 pounds
• Pumpkin seeds: 8 pounds