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Finding the Fourth Proportional to 1,604.86, 2,407.30 and 509.23

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Solution

The fourth proportional to 1,604.86, 2,407.30 and 509.23 is: 763.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,604.86 : 2,407.30 = 509.23 : x
  2. Step 2: Convert to fraction form
    1,604.86/2,407.30 = 509.23/x
  3. Step 3: Cross multiply
    1,604.86x = 2,407.30 × 509.23
  4. Step 4: Simplify right side
    1,604.86x = 1,225,862.09
  5. Step 5: Solve for x
    x = 1,225,862.09/1,604.86
  6. Step 6: Final answer
    x = 763.84

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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.