Which of the following ratios is the greatest?

Options

A. `7:15`
B. `15:23`
C. `17:25`
D. `21:29`

Answer

To determine which of the following ratios is the greatest, we will analyze the given ratios step by step.

Let's denote the ratios as follows:

1. \( \frac{7}{15} \)
2. \( \frac{15}{23} \)
3. \( \frac{17}{25} \)
4. \( \frac{21}{29} \)

### Step 1: Calculate the differences between the antecedents and the consequents of each ratio.

- For \( \frac{7}{15} \):
\[ 15 - 7 = 8 \]

- For \( \frac{15}{23} \):
\[ 23 - 15 = 8 \]

- For \( \frac{17}{25} \):
\[ 25 - 17 = 8 \]

- For \( \frac{21}{29} \):
\[ 29 - 21 = 8 \]

### Step 2: Compare the antecedents of the ratios.

Since all the ratios have the same difference of 8 between the antecedent and the consequent, we can compare the antecedents directly:

- Antecedents are: 7, 15, 17, and 21.

### Step 3: Identify the greatest antecedent.

Among the antecedents:
- The greatest antecedent is 21.

### Step 4: Determine the greatest ratio.

The ratio with the greatest antecedent is:
\[ \frac{21}{29} \]

Thus, the greatest ratio among the given options is \( \frac{21}{29} \).

### Final Answer:
The greatest ratio is \( \frac{21}{29} \).

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