Problem Analysis:
The task involves defining a variable and creating a table to organize information about the prices, quantities, and total prices of three items: herbs, black tea, and blended tea. The goal is to fill in the table step by step, using the given information and relationships between the variables.
#### Given Information:
1.
Herbs:
- Price per pound: $7
- Number of pounds: 17
- Total price: \( 7 \times 17 \)
2.
Black tea:
- Price per pound: $16.25
- Number of pounds: \( x \)
- Total price: \( 16.25 \times x \)
3.
Blended tea:
- Price per pound: $14.4
- Number of pounds: \( 17 + x \)
- Total price: \( 14.4 \times (17 + x) \)
#### Steps to Solve:
We are asked to:
1. Define a variable for the quantity of herbs.
2. Fill in the first two columns of the table with known information.
3. Use the relationship between the quantities to complete the second column.
4. Multiply across to fill in the third column.
Step-by-Step Solution:
#### Step 1: Define the Variable
Let \( x \) represent the number of pounds of black tea.
#### Step 2: Fill in the First Two Columns
From the problem statement:
- Herbs: 17 pounds
- Black tea: \( x \) pounds
- Blended tea: \( 17 + x \) pounds
The first two columns of the table are filled as follows:
| Price per pound | Number of pounds | Total price |
|------------------|-------------------|-------------|
| 7 | 17 | |
| 16.25 | \( x \) | |
| 14.4 | \( 17 + x \) | |
#### Step 3: Complete the Second Column
The second column is already filled based on the given information:
- Herbs: 17 pounds
- Black tea: \( x \) pounds
- Blended tea: \( 17 + x \) pounds
#### Step 4: Multiply Across to Fill in the Third Column
To find the total price for each item, multiply the "Price per pound" by the "Number of pounds":
1.
Herbs:
\[
\text{Total price} = 7 \times 17 = 119
\]
2.
Black tea:
\[
\text{Total price} = 16.25 \times x = 16.25x
\]
3.
Blended tea:
\[
\text{Total price} = 14.4 \times (17 + x) = 14.4 \times 17 + 14.4 \times x = 244.8 + 14.4x
\]
#### Final Table:
| Price per pound | Number of pounds | Total price |
|------------------|-------------------|-------------|
| 7 | 17 | 119 |
| 16.25 | \( x \) | \( 16.25x \)|
| 14.4 | \( 17 + x \) | \( 244.8 + 14.4x \) |
Final Answer:
\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Price per pound} & \text{Number of pounds} & \text{Total price} \\
\hline
7 & 17 & 119 \\
\hline
16.25 & x & 16.25x \\
\hline
14.4 & 17 + x & 244.8 + 14.4x \\
\hline
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of weighted averages worksheet.
