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Finding the Third Proportional to 456.75 and 689.06

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Solution

The third proportional to 456.75 and 689.06 is: 1,039.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.75 : 689.06 = 689.06 : x
  2. Step 2: Convert to fraction form
    456.75/689.06 = 689.06/x
  3. Step 3: Cross multiply
    456.75x = 689.06 × 689.06
  4. Step 4: Simplify right side
    456.75x = 474,807.13
  5. Step 5: Solve for x
    x = 474,807.13/456.75
  6. Step 6: Final answer
    x = 1,039.53

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.