Finding the Third Proportional to 827.72 and 1,742.34

Step by Step Solution

1. Step 1: Write the proportion equation
   827.72 : 1,742.34 = 1,742.34 : x
2. Step 2: Convert to fraction form
   827.72/1,742.34 = 1,742.34/x
3. Step 3: Cross multiply
   827.72x = 1,742.34 × 1,742.34
4. Step 4: Simplify right side
   827.72x = 3,035,761.74
5. Step 5: Solve for x
   x = 3,035,761.74/827.72
6. Step 6: Final answer
   x = 3,667.62