Question

3a=5b and 6b=7c what is the value of a:b:c

Answer 1

Answer:

==> first ...find the common term.

==> in both equations , b is the common term.

==> now find LCM of coefficient of b from both eqns...

==> in 1st eqn ===> 5b

==> in 2nd eqn===> 6b

==> LCM = 5*6 = 30

==> now make 30 b in both eqns ....for that

multiply 1st eqn with 6 and 2nd eqn with 5

===> 18 a = 30 b and 30 b = 35 c

now combine both eqns ===> 18a = 30b = 35c.

now a:b:c ==> 18:30:35

Answer 2

SOLUTION

GIVEN

3a = 5b and 6b = 7c

TO DETERMINE

The value of a : b : c

EVALUATION

Here it is given that 3a = 5b and 6b = 7c

$\sf{3a = 5b} \: \: \: \: gives$

$\displaystyle \sf{a = \frac{5b}{3} }$

$\displaystyle \sf{6b = 7c } \: \: \: \: \: gives$

$\displaystyle \sf{c = \frac{6b}{7} }$

Now

$\displaystyle \sf{a : b : c}$

$= \displaystyle \sf{ \frac{5b}{3} : b : \frac{6b}{7} }$

$= \displaystyle \sf{ \frac{5}{3} : 1: \frac{6}{7} }$

$= \displaystyle \sf{ \bigg( \frac{5}{3} \times 21\bigg) : (1 \times 21): \bigg( \frac{6}{7} \times 21 \bigg)}$

$= \displaystyle \sf{ 35 :21: 18 }$

FINAL ANSWER

$\boxed{ \displaystyle \sf{ \: \: a : b :c = 35 :21: 18 } \: \: }$

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