Question

Lady Edith bought several necklaces at the jewelry store, and each necklace cost 16 dollars. Lady Mary also purchased several necklaces, at a cost of \(\$\)20 each. If the ratio of the number of necklaces Lady Edith purchased to the number of necklaces Lady Mary purchased is 3 to 2, what is the average cost of the necklaces purchased by Lady Edith and Lady Mary? 
 

• A. 16.7
• B. 17.1
• C. 17.6
• D. 17.9
• E. 18.2

Hint:

For problems involving ratios to find an average, you can use the simplest whole numbers from the ratio (in this case, 3 and 2) for your calculation. The average will be the same regardless of the actual number of items, as long as the ratio is maintained.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept: 
The question asks for the average cost of all necklaces purchased by Lady Edith and Lady Mary. This is a weighted average problem because the two sets of necklaces have different costs and were purchased in different quantities. The average cost is the total cost of all necklaces divided by the total number of necklaces. 
 

Step 2: Key Formula or Approach: 
The formula for the average cost is: \[ \text{Average Cost} = \frac{\text{Total Cost}}{\text{Total Number of Items}} \] The total cost is the sum of the costs of necklaces purchased by both individuals. 
 

Step 3: Detailed Explanation: 
The ratio of the number of necklaces purchased by Lady Edith to Lady Mary is 3 to 2. We can assume the simplest case where Lady Edith bought 3 necklaces and Lady Mary bought 2 necklaces. The ratio will hold true for any multiple (e.g., 6 and 4), and the average cost will remain the same. 
First, calculate the total cost for Lady Edith: 
\[ \text{Cost for Edith} = (\text{Number of necklaces}) \times (\text{Cost per necklace}) = 3 \times \$16 = \$48 \] Next, calculate the total cost for Lady Mary: 
\[ \text{Cost for Mary} = (\text{Number of necklaces}) \times (\text{Cost per necklace}) = 2 \times \$20 = \$40 \] Now, find the total cost and total number of necklaces for both: 
\[ \text{Total Cost} = \text{Cost for Edith} + \text{Cost for Mary} = \$48 + \$40 = \$88 \] \[ \text{Total Number of Necklaces} = 3 + 2 = 5 \] Finally, calculate the average cost: 
\[ \text{Average Cost} = \frac{\text{Total Cost}}{\text{Total Number of Necklaces}} = \frac{\$88}{5} = \$17.6 \] 

Step 4: Final Answer 
The average cost of the necklaces is \(\$\)17.6.