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Chapter 1: Problem 73

At what point is the temperature in \({ }^{\circ} \mathrm{F}\) exactly twice that in \({ }^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
Answer: At 160°C and 320°F.

Step by step solution

01

Write down the formula to convert Celsius to Fahrenheit

The formula to convert Celsius to Fahrenheit is: °F = (9/5) * °C + 32
02

Create an equation relating the Fahrenheit and Celsius temperatures

According to the problem, we want to find the point where °F is twice the value of °C, so we can write the equation: °F = 2 * °C
03

Substitute the conversion formula for Fahrenheit into the equation

Now we can substitute the °F conversion formula into the equation: (9/5) * °C + 32 = 2 * °C
04

Solve the equation for Celsius temperature

Subtract (9/5) * °C from both sides of the equation to isolate the Celsius term and simplify the equation: 32 = 2 * °C - (9/5) * °C 32 = (1/5) * °C To solve for °C, multiply both sides by 5: °C = 160
05

Convert the Celsius temperature back into Fahrenheit

Use the conversion formula to find the Fahrenheit temperature when the Celsius temperature is 160: °F = (9/5) * °C + 32 °F = (9/5) * 160 + 32 °F = 288 + 32 °F = 320 At the point where Fahrenheit is exactly twice the Celsius temperature, the temperature is 160° Celsius and 320° Fahrenheit.

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