Question

What is the solution to the proportion \[\dfrac{x}{2} = \dfrac{5}{{15}}\]?

Answer 1

Hint: Two numbers are said to be proportional to each other, if one number has a constant ratio to another number.
The proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
i.e. if the ratio \[\dfrac{y}{x}\] of two variables \[\left( {x{\text{ }}\& y} \right)\] is equal to a constant $k$, then the variable in the numerator of the ratio \[(y)\] is the product of the other variable and the constant
\[y = k \times x\] .
 In this case $y$ is said to be directly proportional to $x$ with proportionality constant $k$.
If \[a,{\text{ }}b,{\text{ }}c,{\text{ }}d\] are proportional , then they will have the same proportionality constant.
(i.e.) \[\dfrac{a}{b} = \dfrac{c}{d}\]
We will apply the same in our given proportion and we will get an equation.
Then by cross multiplication of the terms, we will get the value of $x$ .

Complete step-by-step solution:
It is given that, \[\dfrac{x}{2} = \dfrac{5}{{15}}\] are in proportion.
We need to find out the value of $x$.
Now , we solve it by a special method,
Multiply the known corners and divide by the third number.
\[x = \dfrac{{2 \times 5}}{{15}}\]
On solving the above equation, we have,
\[x = \dfrac{{10}}{{15}}\]
 Hence, \[x = \dfrac{{10}}{{15}}\].
Now , we will divide the numerator and denominator by the common term, we get,
Hence the value of $x$ is \[\dfrac{2}{3}\] which is the required answer for the given question.

Note: If \[x,{\text{ }}y,{\text{ }}z\] are in proportion then, \[\dfrac{x}{y} = \dfrac{y}{z}\] .
If\[a,{\text{ }}b,{\text{ }}c,{\text{ }}d\] are proportional, then they will have the same proportionality constant.
(i.e.)\[\dfrac{a}{b} = \dfrac{c}{d}\].
Here we can also elaborate the problem as equivalent fractions that means their simplified forms are equal.