5. Fran buys socks in packages that contain 9 pairs of white socks for every 3 pairs of blue socks. Mia buys socks in packages with a ratio of 2 blue pairs to 4 white pairs. If the girls each bought 6 pairs of blue socks, how many pairs of white socks would each have bought?

Part A: Complete the ratio tables.

Fran's Sock Packages
| White Socks | Blue Socks |
| ----------- | ---------- |
| [tex]$\square$[/tex] | 3 |
| [tex]$\square$[/tex] | 6 |
| [tex]$\square$[/tex] | 9 |

Mia's Sock Packages
| White Socks | Blue Socks |
| ----------- | ---------- |
| [tex]$\square$[/tex] | 2 |
| [tex]$\square$[/tex] | 4 |
| [tex]$\square$[/tex] | 6 |

Part B: Explain how you can solve this problem.
[tex]$\square$[/tex]



Answer :

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.