Sure, let's break down the problem step by step to arrive at the solution.
### Part A: Complete the ratio tables
First, let's establish the ratios given for each person.
Fran's Sock Packages:
- The ratio of white socks to blue socks is 9:3.
| White Socks | Blue Socks |
|-------------|------------|
| 9 | 3 |
Mia's Sock Packages:
- The ratio of white socks to blue socks is 4:2.
| White Socks | Blue Socks |
|-------------|------------|
| 4 | 2 |
### Part B: Explain how you can solve this problem
1. Identify the Ratios:
- For Fran, the ratio of white socks to blue socks is 9 white socks for every 3 blue socks.
- For Mia, the ratio is 4 white socks for every 2 blue socks.
2. Determine the Number of Blue Socks Purchased:
- Both Fran and Mia bought 6 pairs of blue socks each.
3. Calculate the Number of White Socks Purchased for Fran:
- First, we need to determine the ratio of white socks to blue socks in terms of number of blue socks Fran bought.
- Given the ratio 9:3, simplify it to 3:1.
- This means Fran buys 3 white socks for every 1 blue sock.
- Since Fran bought 6 blue socks, we multiply 6 by the white sock part of the ratio:
[tex]\[
6 \, \text{blue socks} \times 3 \, \text{white socks per blue sock} = 18 \, \text{white socks}
\][/tex]
4. Calculate the Number of White Socks Purchased for Mia:
- Similarly, simplify Mia's ratio 4:2 to 2:1.
- This means Mia buys 2 white socks for every 1 blue sock.
- Since Mia bought 6 blue socks, we multiply 6 by the white sock part of the ratio:
[tex]\[
6 \, \text{blue socks} \times 2 \, \text{white socks per blue sock} = 12 \, \text{white socks}
\][/tex]
### Completed Ratio Tables
Fran's Sock Packages:
| White Socks | Blue Socks |
|-------------|------------|
| 18 | 6 |
Mia's Sock Packages:
| White Socks | Blue Socks |
|-------------|------------|
| 12 | 6 |
### In summary
- Fran would have bought 18 pairs of white socks.
- Mia would have bought 12 pairs of white socks.
