On an old temperature scale known as the Lentigo Scale, the boiling point of water is 85°L and the freezing point is −10°L. To what temperature on the Fahrenheit scale would a temperature of −50°L correspond? Assume that the Lentigo scale is linear; that is, the size of an L degree is the same everywhere on the L scale.

Question

On an old temperature scale known as the Lentigo Scale, the boiling point of water is 85°L and the freezing point is −10°L. To what temperature on the Fahrenheit scale would a temperature of −50°L correspond? Assume that the Lentigo scale is linear; that is, the size of an L degree is the same everywhere on the L scale.

Answer 1

To find the temperature on the Fahrenheit scale corresponding to -50°L on the Lentigo Scale, we need to determine the linear relationship between the Lentigo scale and the Fahrenheit scale.

First, we calculate the difference in freezing and boiling points on the Lentigo scale:
Difference = Boiling point - Freezing point
Difference = 85°L - (-10°L)
Difference = 95°L

Next, we calculate the difference in freezing and boiling points on the Fahrenheit scale:
Difference = Boiling point - Freezing point
Difference = 212°F - 32°F
Difference = 180°F

Now, we can find the size of 1 degree on the Lentigo scale in terms of Fahrenheit:
Lentigo degree / Fahrenheit degree = Difference in Lentigo scale / Difference in Fahrenheit scale
Lentigo degree / Fahrenheit degree = 95°L / 180°F

Now, we can find the temperature on the Fahrenheit scale corresponding to -50°L on the Lentigo scale:
Temperature on Fahrenheit scale = Fahrenheit degree * Number of Lentigo degrees
Temperature on Fahrenheit scale = (95/180) * (-50)
Temperature on Fahrenheit scale = (-95/180) * 50
Temperature on Fahrenheit scale = -26.39°F

Therefore, a temperature of -50°L on the Lentigo scale would correspond to approximately -26.39°F on the Fahrenheit scale.

Answer 2

To convert a temperature from the Lentigo scale to the Fahrenheit scale, we need to determine the difference between the freezing point and boiling point on the Lentigo scale, and the corresponding difference on the Fahrenheit scale.

1. Determine the difference between the freezing point and boiling point on the Lentigo scale:
Lentigo boiling point (85°L) - Lentigo freezing point (-10°L) = 95°L

2. Determine the difference between the freezing point and boiling point on the Fahrenheit scale:
Fahrenheit boiling point (212°F) - Fahrenheit freezing point (32°F) = 180°F

3. Calculate the equivalent temperature on the Fahrenheit scale:
Lentigo temperature (-50°L) * (180°F / 95°L) = -94.74°F

Therefore, a temperature of -50°L on the Lentigo Scale would correspond to approximately -94.74°F on the Fahrenheit scale.