Question

An order of cashews and peanuts weighs 11 pounds and costs $31.
Cashews: $3.00 per pound
Peanuts: $2.50 per pound
How many pounds of cashews and peanuts are in this order?
Start by writing an expression to represent the cost of c pounds of cashews. Keep in mind that 1 pound of cashews costs $3.00
Cost of c
pounds of
cashews
+
Cost of p pounds of peanuts
=
Total Cost
+
?
=
?
Great job!
Now, add an expression to represent the cost of p pounds of peanuts. Keep in mind that 1 pound of peanuts costs $2.50.
Cost of
c
pounds of cashews
+
Cost
of
p
pounds of
peanuts
=
Total Cost
3c
+
=
?
You got it!
Finally, what do you need to set the expression equal to? Reread the problem to determine the total cost of the order.
Cost of cashews
+
Cost of peanuts
=
Total
Cost
3c
+
2.5p
=

Answer 1

The total cost of the order is given as $31. Therefore, we can set up the equation as follows:

\[ 3c + 2.5p = 31 \]

Now, we also know from the problem that the total weight of the cashews and peanuts is 11 pounds. We can express this with another equation:

\[ c + p = 11 \]

Now we have a system of two equations:

1. \( 3c + 2.5p = 31 \)
2. \( c + p = 11 \)

We can solve this system to find the values of \( c \) (pounds of cashews) and \( p \) (pounds of peanuts).

From the second equation, we can solve for \( p \):

\[ p = 11 - c \]

Now, we can substitute \( p \) into the first equation:

\[ 3c + 2.5(11 - c) = 31 \]

Now, distribute the \( 2.5 \):

\[ 3c + 27.5 - 2.5c = 31 \]

Combine like terms:

\[ 0.5c + 27.5 = 31 \]

Now, isolate \( c \):

\[ 0.5c = 31 - 27.5 \]
\[ 0.5c = 3.5 \]
\[ c = \frac{3.5}{0.5} \]
\[ c = 7 \]

Now that we know \( c = 7 \), we can find \( p \):

\[ p = 11 - c = 11 - 7 = 4 \]

So, the order consists of:

- **7 pounds of cashews**
- **4 pounds of peanuts**