Question

If a/b = c/d = e/f = k, prove that each ratio is equal to a + c + e/b + d + f
(easy question!!)

Answer 1

Step-by-step explanation:

Given :

$\rightarrow \bold{\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{e}{f} =k }$

To prove :

Each ratio is equal to  $\bold{\dfrac{a+c+e}{b+d+f} }$

Solution :

Let  $\bold{\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{e}{f}=k }$

Each ratio :

• Sum of antecedents/Sum of consequents

Then we have :

• a = bk
• c = dk
• e = fk

∴ We get :

$\rightarrow \bold{\dfrac{a+c+e}{b+d+f}=\dfrac{bk+dk+fk}{b+d+f} }$

$\rightarrow \bold{\dfrac{k(b+d+f)}{(b+d+f) }=k}$

Hence, each ratio = $\bold{\dfrac{a+c+e}{b+d+f} }$

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