Question

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

• A. 78$^{\circ}$W
• B. 117$^{\circ}$W
• C. 200$^{\circ}$W
• D. 139$^{\circ}$W

Answer 1

The Correct Option is B

 To solve this problem, we need to determine the relationship between the Celsius and W scales of temperature. The problem states that both scales are linear, which implies a linear transformation between them.

We are given:

• Freezing point of water: 0°C corresponds to 39°W
• Boiling point of water: 100°C corresponds to 239°W

This can be expressed with the equation of a line \(y = mx + c\), where \(m\) is the slope of the line and \(c\) is the y-intercept.

To find the slope \(m\), we use the two points:

• Point 1: \((0, 39)\)
• Point 2: \((100, 239)\)

Calculate the slope \(m\):

\(m = \frac{239 - 39}{100 - 0} = \frac{200}{100} = 2\)

The linear equation relating W and Celsius temperature scales is:

\(W = 2C + 39\)

Now, substitute \(C = 39^\circ\) into the equation to find the corresponding W scale temperature:

\(W = 2(39) + 39 = 78 + 39 = 117\)

Thus, a temperature of 39°C on the Celsius scale corresponds to 117°W on the W scale.

Therefore, the correct answer is

117$^{\circ}$W

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