Question

please answer!!!
I am confused ​

Answer 1

$\huge\underline{\underline{\mathfrak{\red{\sf{Answer-}}}}}$

$\sf{a:b:c=6:8:9}$

$\huge\underline{\underline{\mathfrak{\red{\sf{Explanation-}}}}}$

Given :

• $\sf{a:b=3:4}$
• $\sf{b:c=8:9}$

To find :

• $\sf{a:b:c}$

Solution :

It is given that,

$\sf{a:b=3:4}$

Multiplying a and b by 2.

$\implies$ $\sf{3×2:4×2}$

$\implies$ $\sf{6:8}$ ______(1)

Also, it is given that,

$\sf{b:c=8:9}$______(2)

From (1) and (2),

If we notice that, 8 is common among both.

So by combining (1) and (2), we get,

$\green{\sf{a:b:c=6:8:9}}$ ( required answer )

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Answer 2

Question:

If a:b = 3:4 and b:c = 8:9, find a:b:c.

Answer:

a:b:c = 6:8:9.

Note:

• In a ratio, its first term is called antecedent and the second term is called consequent.

• If the simplest form of two or more ratios are same , then they are said to be equivalent ratios.

• Method to find combined ratio :

Step1 : Find the LCM of consequent of first ratio and antecedent of second ratio.

Step2 : Now make the equivalent ratios of both the given ratios such that the consequent of first ratio and the antecedent of second ratio are equal to the obtained LCM.

Step3 : Now finally combine both the ratios.

Solution:

It is given that ;

a:b = 3:4

b:c = 8:9

Let's find the combined ratio of a:b and b:c

(ie; a:b:c)

Step : 1

Here ,

The consequent (second term) of first ratio

(ie; a:b) is 4.

And the antecedent (first term) of second ratio

(ie; b:c) is 8.

Also , the LCM(4,8) = 8

Step : 2

Try to make the consequent of first ratio and antecedent of second ratio equal to there LCM.

Now,

=> a:b = 3:4

=> a:b = (3×2):(4×2)

=> a:b = 6:8

Also;

=> b:c = 8:9

=> b:c = (8×1):(9×1)

=> b:c = 8:9

Hence,

The obtained equivalent ratios are ;

a:b = 6:8 and b:c = 8:9.

Step : 3

Now,

Combine the equivalent ratios a:b = 6:8 and

b:c = 8:9.

Hence,

The combined ratio will be ;

a:b:c = 6:8:9.

Hence,

Required ratio is ; a:b:c = 6:8:9.