Problem: If m/n=4/3m / n=4 / 3m/n=4/3 and r/t=9/14r / t=9 / 14r/t=9/14, the value of 3mr−nt4nt−7mr\dfrac{3 m r-n t}{4 n t-7 m r}4nt−7mr3mr−nt is:
Answer Choices:
A. −512-5 \dfrac{1}{2}−521
B. −1114-\dfrac{11}{14}−1411
C. −114-1 \dfrac{1}{4}−141
D. 1114\dfrac{11}{14}1411
E. −23-\dfrac{2}{3}−32 Solution:
mrnt=43⋅914=67;∴mr=6k\dfrac{m r}{n t}=\dfrac{4}{3} \cdot \dfrac{9}{14}=\dfrac{6}{7} ; \quad \therefore m r=6 k \quadntmr=34⋅149=76;∴mr=6k and nt=7k\quad n t=7 knt=7k.
∴3mr−nt4nt−7mr=18k−7k28k−42k=11k−14k=−1114\therefore \dfrac{3 m r-n t}{4 n t-7 m r}=\dfrac{18 k-7 k}{28 k-42 k}=\dfrac{11 k}{-14 k}=-\dfrac{11}{14}∴4nt−7mr3mr−nt=28k−42k18k−7k=−14k11k=−1411.