Although large mammals like elephants and whales tend to live longer than small ones like mice, larger breeds of dogs...

Phase 1: Owning the Dataset

Understanding the Relationship

The researcher found that for every 2 kg of body mass, life span decreases by 1 month. Let's visualize this on a number line:

Body Mass (kg):    0 -------- 10 -------- 20 -------- 30 -------- 40
Life Span Change:          Base       -5 months    -10 months
                                   (from 10 kg)   (from 10 kg)

This linear relationship means:

• If we move from 10 kg to 12 kg (+2 kg), life span decreases by 1 month
• If we move from 10 kg to 20 kg (+10 kg), life span decreases by 5 months
• The formula: Life span change = \(-\frac{\mathrm{Body\ mass\ change}}{2}\) months

Phase 2: Understanding the Question

The question states: "the average life span of a breed with an average body mass of x kg is y months less than the average life span of a breed with an average body mass of 10 kg."

Breaking this down:

1. We have a reference breed at 10 kg
2. We have another breed at x kg
3. The x kg breed lives y months less than the 10 kg breed

From our relationship, if a breed weighs x kg instead of 10 kg:

• The mass difference is \((\mathrm{x} - 10)\) kg
• The life span difference is \(\frac{(\mathrm{x} - 10)}{2}\) months

Therefore: \(\mathrm{y} = \frac{(\mathrm{x} - 10)}{2}\)

Phase 3: Finding the Answer

We need to find values from our choices [10, 15, 20, 25, 30, 35] where \(\mathrm{y} = \frac{(\mathrm{x} - 10)}{2}\).

Starting systematically:

• If x = 10: \(\mathrm{y} = \frac{(10-10)}{2} = 0\) (not in choices)
• If x = 15: \(\mathrm{y} = \frac{(15-10)}{2} = 2.5\) (not in choices)
• If x = 20: \(\mathrm{y} = \frac{(20-10)}{2} = 5\) (not in choices)
• If x = 25: \(\mathrm{y} = \frac{(25-10)}{2} = 7.5\) (not in choices)
• If x = 30: \(\mathrm{y} = \frac{(30-10)}{2} = 10\) ✓ (10 is in choices!)

Stop here - we found our answer.

Let's verify: A breed with 30 kg average body mass has 20 kg more mass than a 10 kg breed. Since life span decreases by 1 month per 2 kg increase, the life span difference is \(20 \div 2 = 10\) months.

Phase 4: Solution

x = 30
y = 10

A breed with an average body mass of 30 kg has an average life span that is 10 months less than a breed with an average body mass of 10 kg, perfectly matching the researcher's conclusion.