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
=
Nice!
What equation could we write to represent that the number of pounds of sunflower seeds and the number of pounds of pumpkin seeds weighed a total of 20 pounds? Let s represent the number of pounds of sunflower seeds and p represent the number of pounds of pumpkin seeds.
Cost of sunflower seeds
+
Cost of pumpkin seeds
=
Total
Cost
0.75s
+
0.5p
=
13
Number of
pounds of sunflower seeds
+
Number of
pounds of pumpkin seeds
=
Total weight
of the order
+
=

Answer 1

Let's represent the number of pounds of sunflower seeds as \( s \) and the number of pounds of pumpkin seeds as \( p \).

From the problem, we have two equations based on the information given:

1. Cost Equation: The total cost of the sunflower seeds and pumpkin seeds is $13. The expressions for the cost are:

   • Cost of sunflower seeds: \( 0.75s \) (since each pound costs $0.75)
   • Cost of pumpkin seeds: \( 0.50p \) (since each pound costs $0.50)

   So the cost equation is: \[ 0.75s + 0.5p = 13 \]

2. Weight Equation: The total weight of the seeds is 20 pounds. Thus, we can write the weight equation as: \[ s + p = 20 \]

Now we have a system of two equations:

1. \( 0.75s + 0.5p = 13 \) (cost equation)
2. \( s + p = 20 \) (weight equation)

You can solve this system of equations to find the values of \( s \) and \( p \).

Let's solve it step-by-step:

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

Now, substitute this expression for \( p \) into the cost equation: \[ 0.75s + 0.5(20 - s) = 13 \]

Now, simplify and solve for \( s \): \[ 0.75s + 10 - 0.5s = 13 \] \[ 0.25s + 10 = 13 \] \[ 0.25s = 3 \] \[ s = 12 \]

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

So, the order contains:

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

Final Answer:

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