Question

An order of walnuts and almonds weighs 14 pounds and costs $44.
Walnuts: $2.00 per pound
Almonds: $4.00 per pound
How many pounds of walnuts and almonds are in this order?
Start by writing an expression to represent the cost of w pounds of walnuts. Keep in mind that 1 pound of walnuts costs $2.00
Cost of w
pounds of
walnuts
+
Cost of a pounds of almonds
=
Total Cost
+
?
=
?

Answer 1

Let's denote the number of pounds of walnuts as \( w \) and the number of pounds of almonds as \( a \).

The cost for \( w \) pounds of walnuts, given that walnuts cost $2.00 per pound, can be expressed as:

\[
\text{Cost of } w \text{ pounds of walnuts} = 2w
\]

The cost for \( a \) pounds of almonds, given that almonds cost $4.00 per pound, can be expressed as:

\[
\text{Cost of } a \text{ pounds of almonds} = 4a
\]

We also know that the total cost of the order is $44, so we can write the equation for total cost:

\[
2w + 4a = 44
\]

Additionally, we know that the total weight of the nuts is 14 pounds:

\[
w + a = 14
\]

Now we have a system of equations:

1. \( 2w + 4a = 44 \)
2. \( w + a = 14 \)

You can solve this system of equations to find the values of \( w \) and \( a \). To solve the second equation for \( a \), we get:

\[
a = 14 - w
\]

Now we can substitute \( a \) in the first equation:

\[
2w + 4(14 - w) = 44
\]

Distributing the 4:

\[
2w + 56 - 4w = 44
\]

Combining like terms:

\[
-2w + 56 = 44
\]

Subtracting 56 from both sides:

\[
-2w = 44 - 56
\]

\[
-2w = -12
\]

Dividing both sides by -2:

\[
w = 6
\]

Now, substituting \( w \) back into the equation for \( a \):

\[
a = 14 - w = 14 - 6 = 8
\]

So, the order consists of:

- **Walnuts:** 6 pounds
- **Almonds:** 8 pounds

In summary:
- Number of pounds of walnuts: \( 6 \)
- Number of pounds of almonds: \( 8 \)