Question

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