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Finding the Third Proportional to 7,710 and 15,784

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Solution

The third proportional to 7,710 and 15,784 is: 32,313.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,710 : 15,784 = 15,784 : x
  2. Step 2: Convert to fraction form
    7,710/15,784 = 15,784/x
  3. Step 3: Cross multiply
    7,710x = 15,784 × 15,784
  4. Step 4: Simplify right side
    7,710x = 249,134,656
  5. Step 5: Solve for x
    x = 249,134,656/7,710
  6. Step 6: Final answer
    x = 32,313.18

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.