Question

How do you solve $\dfrac{5}{4}=\dfrac{10}{x}$.

Answer 1

Hint: Ratios can be simplified just like fractions. So, in order to solve this question first we will multiply both sides by 4. Then we will multiply the obtained equation by x. Then simplify the obtained equation further to get the value of x.

Complete step-by-step solution:
We have been given an equation $\dfrac{5}{4}=\dfrac{10}{x}$.
We have to solve the given equation and find the value of x.
We can solve the fractions by multiplying or dividing the numerator or denominator of the fraction by a common number.
To solve the equation first we will multiply the equation by 4. Then we will get
$\Rightarrow \dfrac{5}{4}\times 4=\dfrac{10}{x}\times 4$
Now, simplifying further the above obtained equation we will get
$\Rightarrow 5=\dfrac{40}{x}$
Now, multiply the above equation by x we will get
$\Rightarrow 5x=\dfrac{40}{x}\times x$
Now, simplifying further the above obtained equation we will get
$\Rightarrow 5x=40$
Now, divide the whole equation by 5 to get the value of x. Then we will get
$\Rightarrow \dfrac{5x}{5}=\dfrac{40}{5}$
Now, simplifying further the above obtained equation we will get
$\Rightarrow x=8$
So, on solving $\dfrac{5}{4}=\dfrac{10}{x}$ we get the value as $x=8$

Note: To simplify a ratio divide all numbers in the ratio by the same number until they cannot be divided any more. Alternatively we can directly cross multiply the equation. Then we will get
$\begin{align}
  & \dfrac{5}{4}=\dfrac{10}{x} \\
 & \Rightarrow 5x=10\times 4 \\
\end{align}$
Simplifying the above obtained equation we will get
$\Rightarrow 5x=40$
Now, divide the above obtained equation by 5 we will get
$\begin{align}
  & \Rightarrow \dfrac{5x}{5}=\dfrac{40}{5} \\
 & \Rightarrow x=8 \\
\end{align}$