Question

Compare the ratios 7:4 and 12:5 using the following tables. Finish the tables by filling in the missing values A and B. 7 4 14 8 21 12 28 16 A B 12 5 24 10 36 15 48 20 60 25 Responses A = 35 and B = 20. A = 35 and B = 20 . - no response given A = 32 and B = 18. A = 32 and B = 18 . - no response given A = 35 and B = 18. A = 35 and B = 18 . - no response given A = 32 and B = 20.

Answer 1

To compare the ratios \(7:4\) and \(12:5\), we can analyze the given tables.

For the ratio \(7:4\), the first values in the sequence yield these relationships:

• The first pair is \(7\) and \(4\).
• The second pair is formed by multiplying both parts of the ratio by the same integer. Following the sequence:
  • \(7 \times 2 = 14\) and \(4 \times 2 = 8\)
  • \(7 \times 3 = 21\) and \(4 \times 3 = 12\)
  • \(7 \times 4 = 28\) and \(4 \times 4 = 16\)
  • \(7 \times 5 = A\) and \(4 \times 5 = B\)

Now let's calculate \(A\) and \(B\):

• \(A = 7 \times 5 = 35\)
• \(B = 4 \times 5 = 20\)

Next, for the ratio \(12:5\):

• The pairs generated appear to already be complete, so we can confirm \(A\) and \(B\) values:
  • From the pattern above, we see:
    • \(12 \times 5 = 60\), \(5 \times 5 = 25\)

Based on this, we can summarize:

• For the first table, we derive \(A = 35\) and \(B = 20\).
• In this case, both ratios are expressed in consistent multiples.

Thus, the correct answer is:

• A = 35 and B = 20.