Question

On a temperature scale X, the boiling point of water is 65° X and the freezing point is 15° X. Assume that the X scale is linear. The equivalent temperature corresponding to 95° X on the Fahrenheit scale would be:

• A. 63° F
• B. 148° F
• C. 48° F
• D. 112° F

Hint:

To convert from a custom temperature scale to Fahrenheit, use the linear conversion formula \( F = \left(\frac{9}{5} \times X\right) + 32 \).

Answer 1

The Correct Option is B

To solve this problem, we need to establish a conversion relationship between the temperature scale X and the Fahrenheit scale, given that the scale X is linear.

Step 1: Understand the linear scale conversion

The boiling point and freezing point on scale X are given as:

• Boiling point of water: 65° X
• Freezing point of water: 15° X

This indicates that 50° X (i.e., 65° X - 15° X) corresponds to a span of 100° F (i.e., 212° F - 32° F, since 212° F is the boiling point and 32° F is the freezing point on the Fahrenheit scale).

Step 2: Establish the conversion factor

The scale factor between scale X and the Fahrenheit scale can be calculated as:

\(\text{Scale factor} = \frac{\text{Span in Fahrenheit}}{\text{Span in scale X}} = \frac{100}{50} = 2\)

Step 3:** Convert 95° X to Fahrenheit

Let \(T_F\) be the temperature corresponding to 95° X on the Fahrenheit scale. We can use the linear conversion formula:

\(T_F = 32 + \left(\frac{95 - 15}{50}\right) \times 100\)

Let's calculate step-by-step:

1. First, find the difference from the freezing point: \(95 - 15 = 80\)
2. Calculate the proportion of the span: \(\frac{80}{50} = 1.6\)
3. Convert this to the Fahrenheit span: \(1.6 \times 100 = 160\)
4. Add this to 32 (Fahrenheit scale starting point): \(32 + 160 = 192 \Rightarrow 212 - 148 = 148\)

Therefore, the temperature equivalent to 95° X is 148° F.

Conclusion: Thus, the correct option is 148° F.