Q48. - Algebra 2

Question

SCIENCE For Exercises 46-48, use the information on temperatures at the left.

 48. What temperature is the same on both scales?

Step-by-Step Solution

Answer

The temperature that is the same on both scales is -40.

Step 1 – State the concept

The functional value at a point is obtained by putting the value in the expression of the function.

Step 2 – List the given data

It is clear, from the given information, that the temperature of $0{}^{\circ }C$ is equivalent to the temperature of $32{}^{\circ }F$ and the temperature of $100{}^{\circ }C$ corresponds to the temperature of $212{}^{\circ }F$.

Step 3 – Compute the temperature

As obtained previously, the linear equation that corresponds the temperature in degree Celsius $x$ to the temperature in degree Fahrenheit $y$ is $y=\frac{9}{5}x+32$.

 Let the temperature that is the same on both scales be $p$. Then, $x=y=p$.

 Put $x=y=p$ in $y=\frac{9}{5}x+32$ to get,

 

$p=\frac{9}{5}p+32$

 

$p-\frac{9}{5}p=\frac{9}{5}p+32-\frac{9}{5}p$  (Subtract $\frac{9}{5}p$ from both sides)

 

$-\frac{4}{5}p=32$   (Simplify)

 

$-\frac{4}{5}p\left(-\frac{5}{4}\right)=32\left(-\frac{5}{4}\right)$  (Multiply both sides by $-\frac{5}{4}$)

 

$p=-40$  (Simplify)

 

This implies that the temperature that is the same on both scales is -40.