Question

the relationship between the temperature reading f on the fahrenheit scale and the temperature reading c on the celsius scale is given by c = 5/9(f - 32). (a) find the temperature at which the reading is the same on both scales. (b) when is the fahrenheit reading twice the celsius reading?

Explanation:

Step1: Set up equation for (a)

Set $F = C$. Substitute into $C=\frac{5}{9}(F - 32)$. So $F=\frac{5}{9}(F - 32)$.

Step2: Solve the equation for (a)

Expand: $F=\frac{5}{9}F-\frac{160}{9}$. Move terms with $F$ to one - side: $F-\frac{5}{9}F=-\frac{160}{9}$. Combine like terms: $\frac{9F - 5F}{9}=-\frac{160}{9}$, $\frac{4F}{9}=-\frac{160}{9}$. Cross - multiply to get $4F=-160$, then $F=- 40$.

Step3: Set up equation for (b)

Set $F = 2C$. Substitute $C=\frac{5}{9}(F - 32)$ into $F = 2C$, we get $F = 2\times\frac{5}{9}(F - 32)$.

Step4: Solve the equation for (b)

Expand: $F=\frac{10}{9}(F - 32)=\frac{10}{9}F-\frac{320}{9}$. Move terms with $F$ to one - side: $F-\frac{10}{9}F=-\frac{320}{9}$. Combine like terms: $\frac{9F-10F}{9}=-\frac{320}{9}$, $-\frac{F}{9}=-\frac{320}{9}$. Cross - multiply to get $F = 320$.

Answer:

(a) - 40
(b) 320