Use the formula F = 9/5C + 32 to find the Celsius temperature when the Fahrenheit temperature is 90 degrees. Round to the nearest tenth of a degree. Answer: A) 22.2 degrees Celsius B) 67.8 degrees Celsius C) 32.2 degrees Celsius D) 161.5 degrees Celsius
The Correct Answer and Explanation is:
To find the Celsius temperature when the Fahrenheit temperature is 90 degrees, the given formula is: F=95C+32F = \frac{9}{5}C + 32F=59C+32
Substitute 90 for FFF: 90=95C+3290 = \frac{9}{5}C + 3290=59C+32
Subtract 32 from both sides: 90−32=95C90 – 32 = \frac{9}{5}C90−32=59C 58=95C58 = \frac{9}{5}C58=59C
Multiply both sides by 59\frac{5}{9}95: C=59×58C = \frac{5}{9} \times 58C=95×58 C=2909C = \frac{290}{9}C=9290 C≈32.222…C \approx 32.222\ldotsC≈32.222…
Rounded to the nearest tenth, the result is: C≈32.2 degrees CelsiusC \approx 32.2 \, \text{degrees Celsius}C≈32.2degrees Celsius
Correct answer: C) 32.2 degrees Celsius
Explanation:
Converting between Fahrenheit and Celsius uses a linear relationship based on the freezing and boiling points of water. In the Fahrenheit system, water freezes at 32°F and boils at 212°F, while in the Celsius system, water freezes at 0°C and boils at 100°C. The given formula, F=95C+32F = \frac{9}{5}C + 32F=59C+32, rearranges these fixed points into a mathematical expression.
The problem involves finding the original Celsius value that, when placed into the equation, gives 90°F. By isolating the Celsius variable using inverse operations—first subtracting 32, then multiplying by the reciprocal of 95\frac{9}{5}59—the formula is effectively inverted.
Once this value is calculated, the decimal is approximated to the nearest tenth. Decimal rounding is based on the digit in the hundredths place; if that digit is 5 or higher, the tenths place increases by one. In this case, 32.222 rounds to 32.2.
Answer option C matches this calculated value and is therefore correct.
