Express the relationship $4

Question

Express the relationship $4 < C < 18$ in terms of $F$, if $F = \frac { 3 } { 2 } C + 17$.
A) $\quad 24 < F < 45$
B) $\quad 22 < F < 43$
C) $\quad 21 < F < 42$
D) $\quad 27 < F < 40$
E) $\quad 23 < F < 44$

Quizplus · Accepted Answer

Substitute $C=4$ and $C=18$ into the equation for $F$ to get the following inequalities:
$$F=\frac32\cdot 4+17=23 \quad \Longrightarrow \quad 23<F$$
$$F=\frac32\cdot 18+17=44 \quad \Longrightarrow \quad F<44$$
Therefore, the relationship is $23 < F < 44$, which corresponds to answer choice E.

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