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Finding the Third Proportional to 523 and 802.25

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Solution

The third proportional to 523 and 802.25 is: 1,230.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 802.25 = 802.25 : x
  2. Step 2: Convert to fraction form
    523/802.25 = 802.25/x
  3. Step 3: Cross multiply
    523x = 802.25 × 802.25
  4. Step 4: Simplify right side
    523x = 643,605.06
  5. Step 5: Solve for x
    x = 643,605.06/523
  6. Step 6: Final answer
    x = 1,230.60

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.