Browse · harp

smc

algebra senior

Problem

If

\frac{m}{n} = \frac{4}{3}

and

\frac{r}{t} = \frac{9}{14}

, the value of

\frac{3 m r - n t}{4 n t - 7 m r}

is:

(A)

- 5 \frac{1}{2}

(B)

- \frac{11}{14}

(C)

- 1 \frac{1}{4}

(D)

\frac{11}{14}

Solution

From

\frac{m}{n} = \frac{4}{3}

, we have

3 m = 4 n

. From

\frac{r}{t} = \frac{9}{14}

, we have

14 r = 9 t ⟹ 7 r = 4.5 t

This simplifies the fraction to

\frac{4 n r - n t}{4 n t - 7 r \cdot m} ⟹ \frac{4 n r - n t}{4 n t - 4.5 m t} ⟹ \frac{4 n r - n t}{4 n t - 1.5 t \cdot 3 m} ⟹ \frac{4 n r - n t}{4 n r - 1.5 \cdot t \cdot 4 n} ⟹ \frac{\frac{4 \cdot 7 r}{7} t - n t}{4 n t - 6 n t} ⟹ \frac{\frac{4 \cdot 9 t}{7 \cdot 2} n - n t}{- 2 n t} ⟹ \frac{n t ( \frac{36}{14} - 1 )}{- 2 ( n t )} ⟹ \frac{\frac{22}{14}}{- 2} ⟹ - \frac{11}{14}

Final answer

B