Question

1. to make fruit punch, priya mixes 3 scoops of powder with 5 cups of water. mai mixes 4 scoops of powder with 6 cups of water.

a. create a double number line or a table that shows different amounts of powder and water that taste the same as priya’s mixture.

Answer:

for the Table

1. Identify the Ratio: Priya’s ratio of powder to water is \( 3:5 \). This means for every 3 scoops of powder, we need 5 cups of water to maintain the same taste.
2. Find Equivalent Ratios: To find other amounts that taste the same, we multiply both parts of the ratio by the same number. For example, multiplying by 2 gives \( 3\times2 = 6 \) scoops of powder and \( 5\times2 = 10 \) cups of water. Multiplying by 3 gives \( 3\times3 = 9 \) scoops of powder and \( 5\times3 = 15 \) cups of water, and so on. This works because when we scale both the amount of powder and water by the same factor, the concentration of the powder in the water (and thus the taste) remains the same.

If we were to use a double - number line:

• Draw two parallel number lines. Label the top number line "Scoops of Powder" and the bottom one "Cups of Water".
• Mark 3 on the top number line and 5 on the bottom number line (corresponding to Priya's mixture).
• Then, to find other points, we can use the same scale. For example, if we move 3 units to the right on the top number line (to 6), we move 5 units to the right on the bottom number line (to 10). Similarly, moving 6 units to the right on the top (to 9) means moving 10 units to the right on the bottom (to 15), and so forth.

(Note: The table is a more straightforward way to present the equivalent ratios for this problem, but the double - number line follows the same principle of maintaining the 3:5 ratio between powder and water.)