Question

The temperature at which the reading on Fahrenheit scale becomes 90% more than the reading on Celsius scale is

• A. 280 $^\circ$F
• B. 580 $^\circ$F
• C. 608 $^\circ$F
• D. 320 $^\circ$F

Hint:

The relationship between Celsius (C) and Fahrenheit (F) is given by the formula $\frac{C}{5} = \frac{F-32}{9}$. For problems that give another relationship between F and C, set up a system of two equations and solve for the required temperature.

Answer 1

The Correct Option is C

Let F be the temperature reading on the Fahrenheit scale and C be the temperature reading on the Celsius scale.
The problem states that the Fahrenheit reading is 90% more than the Celsius reading.
This can be written as an equation: $F = C + 0.90C = 1.9C$.
The standard conversion formula between Fahrenheit and Celsius is:
$\frac{F-32}{9} = \frac{C}{5}$.
We have a system of two equations with two variables. Substitute the first equation into the second one:
$\frac{1.9C - 32}{9} = \frac{C}{5}$.
Cross-multiply to solve for C:
$5(1.9C - 32) = 9C$.
$9.5C - 160 = 9C$.
$0.5C = 160$.
$C = \frac{160}{0.5} = 320$.
So, the temperature is 320 $^\circ$C.
The question asks for the temperature reading on the Fahrenheit scale. We use the relation $F=1.9C$.
$F = 1.9 \times 320$.
$F = 19 \times 32 = 608$.
So, the temperature is 608 $^\circ$F.