Question

How do you solve $\dfrac{3.4}{x}=\dfrac{2.17}{7.7}$ ?

Answer 1

Hint: For these kinds of questions , we have to make use of basic mathematics. We have to cross -multiply. And then group all the constants. And then find out the value of $x$. Or another way to do this question is by using componendo and dividendo. But we are not going to use it as this will complicate our problem. We are just going to stick with cross-multiplication.

Complete step by step answer:
We have been given an equality, that is : $\dfrac{3.4}{x}=\dfrac{2.17}{7.7}$.
Let us multiply and divide by 10 on both sides. Upon doing so , we get the following :
$\begin{align}
  & \Rightarrow \dfrac{3.4}{x}=\dfrac{2.17}{7.7} \\
 & \Rightarrow \dfrac{3.4\times 10}{10\times x}=\dfrac{2.17\times 10}{7.7\times x} \\
 & \Rightarrow \dfrac{34}{10x}=\dfrac{21.7}{77} \\
\end{align}$
Now we will cross – multiply both sides of the equation. Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow \dfrac{34}{10x}=\dfrac{21.7}{77} \\
 & \Rightarrow 34\times 77=217x \\
\end{align}$
$217$ and $77$ are divisible by $7$ .
So now let us divide the entire equation by $7$ .
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 34\times 77=217x \\
 & \Rightarrow 34\times 11=31x \\
\end{align}$
Now let us multiply the entire equation by $31$ . Upon doing so, we get the following :
$\Rightarrow \dfrac{34\times 11}{31}=x$
Now let us multiply $34\times 11$ . Upon doing so, we get the following :
$\Rightarrow \dfrac{374}{31}=x$
Now let us divide $374$ by $31$ . Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow \dfrac{374}{31}=x \\
 & \Rightarrow x=12.06 \\
\end{align}$

$\therefore $ Hence after solving for $x$ in $\dfrac{3.4}{x}=\dfrac{2.17}{7.7}$ , we get $x=12.06$ .

Note: We have to be alert while solving questions involving decimal points. We have to check carefully the number of digits after each decimal and then proceed accordingly. Even if find a question of the form $\dfrac{a}{b}=\dfrac{c}{d}$ , we should not be in a haste to use componendo and dividendo or just cross - multiplication. We should use what simplifies the question.