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Finding the Fourth Proportional to 1,604.71, 2,407.16 and 509.17

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Solution

The fourth proportional to 1,604.71, 2,407.16 and 509.17 is: 763.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,604.71 : 2,407.16 = 509.17 : x
  2. Step 2: Convert to fraction form
    1,604.71/2,407.16 = 509.17/x
  3. Step 3: Cross multiply
    1,604.71x = 2,407.16 × 509.17
  4. Step 4: Simplify right side
    1,604.71x = 1,225,639.08
  5. Step 5: Solve for x
    x = 1,225,639.08/1,604.71
  6. Step 6: Final answer
    x = 763.78

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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.