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Finding the Third Proportional to 509.06 and 784.69

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Solution

The third proportional to 509.06 and 784.69 is: 1,209.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    509.06 : 784.69 = 784.69 : x
  2. Step 2: Convert to fraction form
    509.06/784.69 = 784.69/x
  3. Step 3: Cross multiply
    509.06x = 784.69 × 784.69
  4. Step 4: Simplify right side
    509.06x = 615,734.47
  5. Step 5: Solve for x
    x = 615,734.47/509.06
  6. Step 6: Final answer
    x = 1,209.55

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.