A new temperature scale has the freezing point of water at 50 degrees and the boiling point of water at 125 degrees. Normal body temperature is 37 degrees C and 98.6 degrees F. Water freezes at 0 degrees C and 32 degrees F and boils at 100 degrees C and 212 degrees F. What is normal body temperature on this new scale?

To determine normal body temperature on the new temperature scale, we need to find the equivalent temperature for 37 degrees Celsius or 98.6 degrees Fahrenheit.

First, let's convert 37 degrees Celsius to Fahrenheit using the formula:
°F = (°C × 9/5) + 32

°F = (37 × 9/5) + 32
°F = 98.6

So, 37 degrees Celsius is equivalent to 98.6 degrees Fahrenheit.

Since we know that the freezing point of water on the new scale is 50 degrees and the boiling point is 125 degrees, we can use these values to find the equivalent temperature for 98.6 degrees Fahrenheit.

Using direct proportionality:
(125 - 50) is equivalent to (98.6 - x)
75 is equivalent to (98.6 - x)

To find x, we can set up a proportion:
75 / (98.6 - x) = 125 / (75)

Cross-multiply to solve for x:
75 * 75 = 125 * (98.6 - x)
5625 = 12325 - 125x
125x = 12325 - 5625
125x = 6700
x = 6700 / 125
x = 53.6

Therefore, normal body temperature on this new temperature scale is approximately 53.6 degrees.