Which table shows equivalent ratios?

Question

A 2-column table with 4 rows. Column 1 is labeled Feet with entries 2, 4, 5, 6. Column 2 is labeled Inches with entries 36, 48, 60, 72.
A 2-column table with 4 rows. Column 1 is labeled Feet with entries 2, 3, 4, 6. Column 2 is labeled Inches with entries 22, 39, 48, 72.
A 2-column table with 4 rows. Column 1 is labeled Feet with entries 2, 5, 6, 7. Column 2 is labeled Inches with entries 24, 60, 72, 84.
A 2-column table with 4 rows. Column 1 is labeled Feet with entries 2, 3, 4, 6. Column 2 is labeled Inches with entries 28, 36, 48, 72.

Answer 1

To determine which table shows equivalent ratios, we need to analyze the relationship between the values in each table. The goal is to see if the ratio of feet to inches remains constant across the entries.

1. Table 1:

   • Feet: 2, 4, 5, 6
   • Inches: 36, 48, 60, 72
   • Ratios:
     • 2 feet: 36 inches (2:36) = 1:18
     • 4 feet: 48 inches (4:48) = 1:12
     • 5 feet: 60 inches (5:60) = 1:12
     • 6 feet: 72 inches (6:72) = 1:12

   Not equivalent.

2. Table 2:

   • Feet: 2, 3, 4, 6
   • Inches: 22, 39, 48, 72
   • Ratios:
     • 2 feet: 22 inches (2:22) = 1:11
     • 3 feet: 39 inches (3:39) = 1:13
     • 4 feet: 48 inches (4:48) = 1:12
     • 6 feet: 72 inches (6:72) = 1:12

   Not equivalent.

3. Table 3:

   • Feet: 2, 5, 6, 7
   • Inches: 24, 60, 72, 84
   • Ratios:
     • 2 feet: 24 inches (2:24) = 1:12
     • 5 feet: 60 inches (5:60) = 1:12
     • 6 feet: 72 inches (6:72) = 1:12
     • 7 feet: 84 inches (7:84) = 1:12

   All are equivalent to 1:12. This is a consistent ratio.

4. Table 4:

   • Feet: 2, 3, 4, 6
   • Inches: 28, 36, 48, 72
   • Ratios:
     • 2 feet: 28 inches (2:28) = 1:14
     • 3 feet: 36 inches (3:36) = 1:12
     • 4 feet: 48 inches (4:48) = 1:12
     • 6 feet: 72 inches (6:72) = 1:12

   Not equivalent.

Conclusion: The table that shows equivalent ratios is Table 3.