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Finding the Third Proportional to 685 and 1,053

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Solution

The third proportional to 685 and 1,053 is: 1,618.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    685 : 1,053 = 1,053 : x
  2. Step 2: Convert to fraction form
    685/1,053 = 1,053/x
  3. Step 3: Cross multiply
    685x = 1,053 × 1,053
  4. Step 4: Simplify right side
    685x = 1,108,809
  5. Step 5: Solve for x
    x = 1,108,809/685
  6. Step 6: Final answer
    x = 1,618.70

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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.