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 find the reading in \(^{\circ}X\) for a temperature of \(60^{\circ}C\), we need to establish a relationship between the Celsius scale and the unknown scale X.<br /><br />The ice-point (0°C) corresponds to \(50^{\circ}X\) and the steam-point (100°C) corresponds to \(200^{\circ}X\).<br /><br />First, determine the conversion formula between the two scales. The range on the Celsius scale from ice-point to steam-point is 100°C (100°C - 0°C). On the X scale, this range is \(200^{\circ}X - 50^{\circ}X = 150^{\circ}X\).<br /><br />The conversion factor between the scales is:<br />\[<br />1^{\circ}C = \frac{150^{\circ}X}{100^{\circ}C} = 1.5^{\circ}X<br />\]<br /><br />Now, convert \(60^{\circ}C\) to the X scale:<br />\[<br />60^{\circ}C = 50^{\circ}X + (60 \times 1.5^{\circ}X)<br />\]<br />\[<br />= 50^{\circ}X + 90^{\circ}X<br />\]<br />\[<br />= 140^{\circ}X<br />\]<br /><br />Therefore, the reading in \(^{\circ}X\) for a temperature of \(60^{\circ}C\) is \(140^{\circ}X\).