1-3a-1-4b-1-6c-and-a-b-c-27-find-a-c-

Question Number 179140 by Shrinava last updated on 25/Oct/22

\frac{1}{3 a} = \frac{1}{4 b} = \frac{1}{6 c} and a + b + c = 27

find a - c = ?

Answered by Frix last updated on 25/Oct/22

a = 4 t

b = 3 t

c = 2 t

a + b + c = 27

9 t = 27

t = 3

a = 12

b = 9

c = 6

a - c = 6

Commented by Frix last updated on 25/Oct/22

yes thank you

Answered by Rasheed.Sindhi last updated on 25/Oct/22

3 a = 4 b = 6 c \land a + b + c = 27; a - c = ?

[_{\underset{}{}} \underset{H e n c e w e n e e d v a l u e o f c}{3 a = 6 c \Rightarrow a - 2 c = 0 \Rightarrow a - c = c}]

▸ E l e m i n a t i n g b f r o m a + b + c = 27

3 a = 4 b = 6 c \Rightarrow {\begin{cases} b = \frac{3}{2} c \\ b = \frac{3}{4} a \end{cases}

∙ a + b + c = 27 \Rightarrow a + \frac{3}{4} a + c = 27

\Rightarrow 7 a + 4 c = 108 \dots . (i)

∙ a + b + c = 27 \Rightarrow a + \frac{3}{2} c + c = 27

\Rightarrow 2 a + 5 c = 54 \dots . (i i)

▸ E l e m i n a t i n g a f r o m (i) & (i i)

{\begin{cases} 2 \times (i) \Rightarrow 14 a + 8 c = 216 \\ 7 \times (i i) \Rightarrow 14 a + 35 c = 378 \end{cases} \Rightarrow 27 c = 162

\Rightarrow c = \frac{162}{27} = 6

∙ 3 a = 6 c \Rightarrow a - 2 c = 0 \Rightarrow a - c = c = 6

Answered by som(math1967) last updated on 25/Oct/22

\frac{1}{3 a} = \frac{1}{4 b} = \frac{1}{6 c}

3 a = 4 b = 6 c

\frac{3 a}{12} = \frac{4 b}{12} = \frac{6 c}{12}

\frac{a}{4} = \frac{b}{3} = \frac{c}{2} = k (l e t)

∴ a = 4 k, b = 3 k, c = 2 k

a + b + c = 27

\Rightarrow 4 k + 3 k + 2 k = 27

\Rightarrow 9 k = 27 \Rightarrow k = 3

a - c = 4 k - 2 k = 2 k = 2 \times 3 = 6

Answered by Rasheed.Sindhi last updated on 25/Oct/22

\frac{1}{3 a} = \frac{1}{4 b} = \frac{1}{6 c} \land a + b + c = 27; a - c = ?

\frac{1}{3 a} = \frac{1}{4 b} = \frac{1}{6 c} \Rightarrow \frac{4 \times 1}{4 (3 a)} = \frac{3 \times 1}{3 (4 b)} = \frac{2 \times 1}{2 (6 c)}

= \frac{9}{12 (a + b + c)} = \frac{3}{4 \times 27} = \frac{1}{36}

3 a = 36 \land 6 c = 36

3 a = 36 \land 3 c = 18

\Rightarrow 3 a - 3 c = 18

\Rightarrow a - c = 6