To determine who will use more water, we need to calculate how much water each will use when they each use 48 cups of flour, based on their respective ratios.

Step 1: Set up the ratios

• Nathan’s ratio: 3 cups of water for every 8 cups of flour
• Cody’s ratio: 4 cups of water for every 12 cups of flour

Step 2: Scale up each ratio to 48 cups of flour

1. For Nathan:

   • $8$ cups of flour corresponds to $3$ cups of water.
   • To find the equivalent amount for $48$ cups of flour, determine the factor needed: $\frac{48}{8} = 6$.
   • Multiply both parts of Nathan’s ratio by $6$: $3 \times 6 = 18 \text{ cups of water}$
   • Therefore, Nathan will use 18 cups of water when he uses 48 cups of flour.

2. For Cody:

   • $12$ cups of flour corresponds to $4$ cups of water.
   • To reach $48$ cups of flour, find the factor: $\frac{48}{12} = 4$.
   • Multiply both parts of Cody’s ratio by $4$: $4 \times 4 = 16 \text{ cups of water}$
   • Therefore, Cody will use 16 cups of water when he uses 48 cups of flour.

Conclusion:

Nathan will use 18 cups of water, and Cody will use 16 cups of water when each uses 48 cups of flour. So, Nathan uses more water.

Correct Answer:

C. Nathan will use 18 cups of water and Cody will only use 16 cups of water, so Nathan will use more cups of water.

Would you like a detailed explanation on equivalent ratios or have any further questions?

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1. How do equivalent ratios work in proportional scaling?
2. Can we solve this using a unit rate approach instead of tables?
3. How do we set up and interpret ratios in real-world problems?
4. Are there shortcuts for comparing ratios without tables?
5. How is this approach used in similar recipe or ingredient problems?

Tip: Always double-check the scaling factor when working with ratios to avoid simple mistakes in calculations.