Questions: The table shows how some lengths in inches are related to their equivalent lengths in centimeters. Inches vs. Centimeters Length (inches) Length (centimeters) 2 5.08 5 12.7 10 25.4 25 63.5 30 ? What number is missing from the last row of the table? A 76.2 B. 88.9 C. 101.6 D. 152.4

Solution Steps

From the table, observe the relationship between inches and centimeters. For example:

• \( 2 \) inches \( = 5.08 \) centimeters
• \( 5 \) inches \( = 12.7 \) centimeters
• \( 10 \) inches \( = 25.4 \) centimeters
• \( 25 \) inches \( = 63.5 \) centimeters

Divide the length in centimeters by the corresponding length in inches to find the conversion factor: \[ \text{Conversion factor} = \frac{5.08}{2} = 2.54 \, \text{cm/inch} \] Verify this with other rows: \[ \frac{12.7}{5} = 2.54, \quad \frac{25.4}{10} = 2.54, \quad \frac{63.5}{25} = 2.54 \] The conversion factor is consistent at \( 2.54 \) cm/inch.

Multiply the length in inches (\( 30 \)) by the conversion factor (\( 2.54 \)) to find the equivalent length in centimeters: \[ 30 \times 2.54 = 76.2 \, \text{cm} \]

Final Answer