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Finding the Fourth Proportional to 1,509.84, 2,264.76 and 414.20

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Solution

The fourth proportional to 1,509.84, 2,264.76 and 414.20 is: 621.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,509.84 : 2,264.76 = 414.20 : x
  2. Step 2: Convert to fraction form
    1,509.84/2,264.76 = 414.20/x
  3. Step 3: Cross multiply
    1,509.84x = 2,264.76 × 414.20
  4. Step 4: Simplify right side
    1,509.84x = 938,069.25
  5. Step 5: Solve for x
    x = 938,069.25/1,509.84
  6. Step 6: Final answer
    x = 621.30

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.