Express the relationship $10

Question

Express the relationship $10 < C < 20$ in terms of $F$, if $F = \frac { 5 } { 2 } C + 11$.
A) $\quad 37 < F < 62$
B) $\quad 34 < F < 59$
C) $\quad 36 < F < 61$
D) $\quad 40 < F < 57$
E) $\quad 35 < F < 60$

Quizplus · Accepted Answer

We can solve for $C$ in terms of $F$ by first subtracting 11 from both sides: $$F-11=\frac{5}{2}C.$$ Then, we can multiply both sides by $\frac{2}{5}$ to obtain: $$\frac{2}{5}(F-11)=C.$$ Therefore, we have: $$10<\frac{2}{5}(F-11)<20.$$ Multiplying all parts of the inequality by $\frac{5}{2}$ (which is positive, so it does not change the direction of the inequality) gives: $$20<5(F-11)<40,$$ or equivalently: $$20<5F-55<40.$$ Adding 55 to all parts of the inequality gives: $$75<5F<95.$$ Finally, dividing all parts of the inequality by 5 (again, since 5 is positive) gives: $$15<F<19.$$ Therefore, the answer is $\boxed{\textbf{(C)}}.$

Express the Relationship 10<C<2010 < C < 2010<C<20 In Terms Of FFF

Express the Relationship $10 < C < 20$ In Terms Of $F$