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Finding the Third Proportional to 410 and 770

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Solution

The third proportional to 410 and 770 is: 1,446.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    410 : 770 = 770 : x
  2. Step 2: Convert to fraction form
    410/770 = 770/x
  3. Step 3: Cross multiply
    410x = 770 × 770
  4. Step 4: Simplify right side
    410x = 592,900
  5. Step 5: Solve for x
    x = 592,900/410
  6. Step 6: Final answer
    x = 1,446.10

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Why These Related Problems?

These problems maintain the same ratio (1.88) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.