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
+
=
Great job!
One way to solve this system is to substitute the value of one variable into the other equation. To do this, we can use either variable, p or s. So, we need to know either: p = some value, so that we can substitute that value for p, or, s = some value, so that we can substitute that value for s. Is either equation written as p equals some value or s equals some value yet?
0.75s+0.5p = 13
s+p = 20

Yes

No

Answer 1

To find the pounds of sunflower seeds (s) and pumpkin seeds (p) in the order, we start with the two equations we've set up based on the problem:

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

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

Now, we can express one variable in terms of the other using the weight equation. Let's solve for \( p \) in terms of \( s \):

\[ p = 20 - s \]

Now that we have \( p \) expressed in terms of \( s \), we can substitute this expression into the first equation (the cost equation):

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

Now, distribute \( 0.5 \) in the equation:

\[ 0.75s + 10 - 0.5s = 13 \]

Next, combine like terms:

\[ (0.75s - 0.5s) + 10 = 13 \] \[ 0.25s + 10 = 13 \]

Now, isolate \( s \) by subtracting 10 from both sides:

\[ 0.25s = 3 \]

To solve for \( s \), divide both sides by 0.25:

\[ s = \frac{3}{0.25} = 12 \]

Now that we have \( s \), we can find \( p \) by plugging \( s \) back into the equation \( p = 20 - s \):

\[ p = 20 - 12 = 8 \]

Thus, the order contains:

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

To summarize:

• \( s = 12 \)
• \( p = 8 \)