Answer
a) $5n-24t+1080=0$
b) $76.25$ Fahrenheit degrees
Work Step by Step
a) Let's note $t=an+b$ the equation relating the temperature $t$ and the number $n$ of chirps per minute.
Let's build a linear system of two equations using the given data:
$$\begin{cases}
70=120a+b\\
80=168a+b.
\end{cases}$$
Use the elimination method:
$$\begin{cases}
-70=-120a-b\\
80=168a+b.
\end{cases}$$
$$\begin{align*}
-70+80&=-120a-b+168a+b\\
10&=48a\\
a&=\dfrac{10}{48}=\dfrac{5}{24}.
\end{align*}$$
We determine $b$:
$$b=70-120\left(\dfrac{5}{24}\right)=45.$$
The equation is:
$$t=\dfrac{5}{24}n+45$$
$$5n-24t+1080=0.\tag1$$
b) We calculate $t$ using $n=150$ in Eq. $(1)$:
$$\begin{align*}
5(150)-24t+1080&=0\\
1830&=24t\\
t&=\dfrac{1830}{24}\\
&=76.25.
\end{align*}$$
