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Finding the Third Proportional to 459.42 and 689.13

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Solution

The third proportional to 459.42 and 689.13 is: 1,033.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    459.42 : 689.13 = 689.13 : x
  2. Step 2: Convert to fraction form
    459.42/689.13 = 689.13/x
  3. Step 3: Cross multiply
    459.42x = 689.13 × 689.13
  4. Step 4: Simplify right side
    459.42x = 474,904.03
  5. Step 5: Solve for x
    x = 474,904.03/459.42
  6. Step 6: Final answer
    x = 1,033.70

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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.