Final Answer:
5 greens are required for 2 blues and 4 whites.
Step-by-step explanation:
Direct Proportion: Blues vary directly with greens (meaning they increase or decrease proportionally).
Inverse Proportion: Blues vary inversely with whites squared (meaning as whites squared increase, blues decrease proportionally).
Set Up Proportion: We can express the relationship as a proportion: B ∝ G / W^2.
Substitute Known Values: We know that when there are 3 greens (G) and 2 whites (W), there are 4 blues (B): 4 ∝ 3 / 2^2.
Solve for Constant of Proportionality: To find the constant of proportionality (k), we can multiply both sides by 4 * 2^2: 4 * 4 = k * 3. Solving for k, we get k = 16/3.
Apply Constant to New Scenario: For 2 blues and 4 whites, we can set up a new proportion: 2 ∝ G / 4^2.
Substitute Constant and Solve for Greens: Replace k with 16/3: 2 ∝ G / 16. Solving for G, we get G = 2 * 16 = 32.
Round to Nearest Whole Number: Since the number of greens should be a whole number, we round 32 up to the nearest whole number: G = 5.
Therefore, 5 greens are required for 2 blues and 4 whites.