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Finding the Third Proportional to 977 and 1,547

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Solution

The third proportional to 977 and 1,547 is: 2,449.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 1,547 = 1,547 : x
  2. Step 2: Convert to fraction form
    977/1,547 = 1,547/x
  3. Step 3: Cross multiply
    977x = 1,547 × 1,547
  4. Step 4: Simplify right side
    977x = 2,393,209
  5. Step 5: Solve for x
    x = 2,393,209/977
  6. Step 6: Final answer
    x = 2,449.55

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.