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Finding the Third Proportional to 213 and 524.25

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Solution

The third proportional to 213 and 524.25 is: 1,290.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 524.25 = 524.25 : x
  2. Step 2: Convert to fraction form
    213/524.25 = 524.25/x
  3. Step 3: Cross multiply
    213x = 524.25 × 524.25
  4. Step 4: Simplify right side
    213x = 274,838.06
  5. Step 5: Solve for x
    x = 274,838.06/213
  6. Step 6: Final answer
    x = 1,290.32

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Why These Related Problems?

These problems maintain the same ratio (2.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.