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On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39° W and 239° W respectively. What will be the temperature on the new scale, corresponding to a temperature of 39°C on the Celsius scale?

1. 78° W
2. 117° W
3. 200° W
4. 139° W

Correct answer: 117° W

Solution

The W scale is linear, so we can use the relation: (T_W - 39)/(239 - 39) = (T_C - 0)/(100 - 0). Substituting T_C = 39°C, we get (T_W - 39)/200 = 39/100. Solving for T_W, T_W = 117° W.

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