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
+
?
=
?
Nice!
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
+
=
?
Good work!
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
=
Great job!
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

To represent the total weight of the order with your variables:

Let \( s \) represent the number of pounds of sunflower seeds and \( p \) represent the number of pounds of pumpkin seeds. The total weight of the order should be 20 pounds. Thus, we can write the equation as:

\[ s + p = 20 \]

Now, summarizing together, we have the following two equations:

1. The cost equation: \[ 0.75s + 0.5p = 13 \]

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

You can solve this system of equations to find the values of \( s \) and \( p \). To do this, you can express \( p \) in terms of \( s \) using the second equation and substitute it into the first equation:

From the second equation:

\[ p = 20 - s \]

Now substitute \( p \) in the first equation:

\[ 0.75s + 0.5(20 - s) = 13 \]

Now solve for \( s \):

\[ 0.75s + 10 - 0.5s = 13 \] \[ 0.25s + 10 = 13 \] \[ 0.25s = 3 \] \[ s = 12 \]

Then substitute \( s \) back to find \( p \):

\[ p = 20 - s = 20 - 12 = 8 \]

So, the order consists of:

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