Question

If $\dfrac{5}{x} = \dfrac{{15}}{{x + 20}}$ , what is the value of $\dfrac{x}{5}$ ?
A. $10$
B. $5$
C. $2$
D. $\dfrac{1}{2}$

Answer 1

Hint: In this question, we are given an equation which we have to solve and find the value of $\dfrac{x}{5}$ .
So, for that first, we will find the value of $x$ , then divide it by $5$ .
To get the value of $x$ , cross multiply the given equation and simplify using basic algebra and distributive laws.

Formula to be used:
Distributive law over addition $a(b + c) = ab + ac$ .

Complete step by step solution:
Given equation $\dfrac{5}{x} = \dfrac{{15}}{{x + 20}}$ .
To find the value of $\dfrac{x}{5}$ , for that, we’ll first find the value of $x$ .
First, cross multiply the given equation, we get, $5(x + 20) = 15x$ .
Now, distributive law over addition, first multiply $5$ by $x$ , then by $20$ , which gives, $5x + 100 = 15x$ .
Now, we need to shift variables on one side and constants on another side, so, for that, subtract $5x$ on both sides, we get, $5x + 100 - 5x = 15x - 5x$ , i.e., $100 = 10x$ , we can also write it as $10x = 100$ .
Now, divide by $10$ on both sides, we get, $\dfrac{{10x}}{{10}} = \dfrac{{100}}{{10}}$ , on solving, we get, $x = 10$ .
Now, we have to find the value of $\dfrac{x}{5}$ , so put $x = 10$ , in this term, we get, $\dfrac{{10}}{5}$ , i.e., $2$ .
Hence, the value of $\dfrac{x}{5} = 2$ .

Note: One needs to know the basics of algebra very well to solve such equations.
If we add or subtract the same terms on both sides of the equality, then the equation does not change. Similarly, if we divide or multiply by the same terms on both sides of the equality, then also the equation does not change.
While solving the question do not skip any of the terms and do not confuse while simplifying.