Answer
a.) $-40°C = -40°F$
b.) $160°C$ and $320°F$
c.) $-11.4°C$ and $+11.4°F$
Work Step by Step
a.) When the Fahrenheit thermometer gives the same reading as the Celsius thermometer;
Let x = the reading on the Celsius thermometer = the reading on the Fahrenheit thermometer
$x °F = 1.8 * (x °C) + 32$
Note that you can write this equation with or without units.
$x = 1.8x + 32$
$1.8x - x = -32$
$\frac{0.8x}{2.8} = \frac{-32}{2.8}$
$x = -40$
Therefore,
x = -40 °C = -40 °F
b.) When a Fahrenheit thermometer give a reading that is twice that on the Celsius
thermometer;
$2x °F = 1.8 * (x °C) + 32$
$2x = 1.8x + 32$
$1.8x - 2x = -32$
$\frac{-0.2x}{0.2} = \frac{-32}{0.2}$
$x = 160 °C$
Therefore,
$x °C = 160 °C$
$2x °F = 320 °F$
c.) When the Fahrenheit thermometer gives a reading that is numerically the same but opposite in sign from that on the Celsius thermometer;
$-x °F = 1.8 * (x °C) + 32$
$-x = 1.8x + 32$
$1.8x + x = -32$
$\frac{2.8x}{0.2} = \frac{-32}{2.8}$
$x = -11.4 °C$
Therefore,
$x °C = -11.4 °C$
$-x °F = -(-11.4) °F = 11.4 °F$
