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Finding the Third Proportional to 656.86 and 1,416.23

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Solution

The third proportional to 656.86 and 1,416.23 is: 3,053.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    656.86 : 1,416.23 = 1,416.23 : x
  2. Step 2: Convert to fraction form
    656.86/1,416.23 = 1,416.23/x
  3. Step 3: Cross multiply
    656.86x = 1,416.23 × 1,416.23
  4. Step 4: Simplify right side
    656.86x = 2,005,719.80
  5. Step 5: Solve for x
    x = 2,005,719.80/656.86
  6. Step 6: Final answer
    x = 3,053.50

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.