Activity: If the ice-point and the steam-point temperatures on an unknown scale X are 50^0X and 200^circ X , respectively, then what is the reading in {}^0X for a temperature of 60^circ C

To convert a temperature from Celsius to the unknown scale X, we need to establish the relationship between the two scales. We know the following points:<br /><br />- Ice point: \(0^{\circ}C = 50^{\circ}X\)<br />- Steam point: \(100^{\circ}C = 200^{\circ}X\)<br /><br />We can use these points to create a linear equation that relates the Celsius temperature (C) to the unknown scale (X).<br /><br />First, let's determine the conversion formula. The general form of the linear equation is:<br />\[ X = aC + b \]<br /><br />Using the given points:<br />1. When \( C = 0 \), \( X = 50 \):<br /> \[ 50 = a(0) + b \]<br /> \[ b = 50 \]<br /><br />2. When \( C = 100 \), \( X = 200 \):<br /> \[ 200 = a(100) + 50 \]<br /> \[ 200 - 50 = 100a \]<br /> \[ 150 = 100a \]<br /> \[ a = \frac{150}{100} = 1.5 \]<br /><br />So, the conversion formula is:<br />\[ X = 1.5C + 50 \]<br /><br />Now, we can find the reading in \( ^{\circ}X \) for a temperature of \( 60^{\circ}C \):<br />\[ X = 1.5(60) + 50 \]<br />\[ X = 90 + 50 \]<br />\[ X = 140 \]<br /><br />Therefore, the reading in \( ^{\circ}X \) for a temperature of \( 60^{\circ}C \) is \( 140^{\circ}X \).