Question

Question was provided via image upload.

Explanation:

Question 1

Step 1: Analyze Priya's Ratio

Priya calculates the ratio of wheat to water as \(6:15\). To find the unit rate (wheat per water), we divide the number of cups of wheat by cups of water: \(\frac{6}{15} = 0.4\). So, 0.4 cups of wheat per cup of water. This is correct.

Step 2: Analyze Han's Ratio

Han calculates the ratio of water to wheat as \(15:6\). To find the unit rate (water per wheat), we divide the number of cups of water by cups of wheat: \(\frac{15}{6} = 2.5\). So, 2.5 cups of water per cup of wheat. This is also correct.

Step 1: Recall the Ratio

From Han's unit rate, we know the ratio of water to wheat is \(2.5\) cups of water per cup of wheat (or from the original ratio \(15:6\), which simplifies to \(2.5:1\) for water to wheat).

Step 2: Calculate Water for 5 Cups Wheat

If 1 cup of wheat needs 2.5 cups of water, then for 5 cups of wheat, we multiply: \(5 \times 2.5 = 12.5\).

Step 1: Recall the Ratio

From Priya's unit rate, we know the ratio of wheat to water is \(0.4\) cups of wheat per cup of water (or from the original ratio \(6:15\), which simplifies to \(0.4:1\) for wheat to water).

Step 2: Calculate Wheat for 10 Cups Water

If 1 cup of water needs 0.4 cups of wheat, then for 10 cups of water, we multiply: \(10 \times 0.4 = 4\).

Answer:

Both Priya and Han are correct. Priya's ratio (wheat to water) gives 0.4 wheat per water, and Han's ratio (water to wheat) gives 2.5 water per wheat, both calculated correctly from the given 6 cups wheat and 15 cups water.

Question 2a