Question

A scientist uses a scale Y for measuring temperature. In this scale, pure water melts at 10 Degrees Y and boils at 130 Degrees Y at standard atmospheric pressure. The scientist measures the temperature at which sodium melts to be 127 Degrees Y. Express this temperature in degrees Celsius.

(A) 97.5 Degrees Celsius
(B) 102.6 Degrees Celsius
(C) 38.6 Degrees Celsius
(D) 196.6 Degrees Celsius

Answer 1

Let:

$$\begin{array}{l} C(0) = 0{}^{\circ} \mathrm{C} \\ C(100) = 100{}^{\circ} \mathrm{C} \\ Y(0) = 10{}^{\circ} \\ Y(100) = 130{}^{\circ} \\ Y(127) = 127{}^{\circ} \\ \end{array}$$ $$C(127) = ?$$

It's possible to present dependence C from Y as equation:

$$C(x) = a * Y(x) + b$$

Write a system of equations:

$$\left\{ \begin{array}{l} 10a + b = 0 \\ 130a + b = 100 \end{array} \right.$$

Solve a system:

$$\left\{ \begin{array}{l} b = -10a \\ 130a + b = 100 \\ b = -10a \\ 130a - 10a = 100 \end{array} \right.$$ $$\left\{ \begin{array}{l} 10a + b = 0 \\ a = \frac{100}{120} \end{array} \right.$$ $$a = \frac{10}{12}, \quad b = -100/12$$

Equation:

$$C(x) = \frac{10}{12} Y(x) - 100/12$$

Enter data:

$$\begin{array}{l} C(127) = 127 \frac{10}{12} - \frac{100}{12} \\ C(127) = 97.5{}^{\circ} \mathrm{C} \\ \end{array}$$

Answer:

"A" - 97.5°C