Question

Find x, if \[x,15,36,27\] are in proportion.

Answer 1

Hint: Two numbers are said to be proportional to each other if one number has a constant ratio to another number.
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".
If the ratio \[\dfrac{y}{x}\] of two variable \(x\) and \(y\) 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 \[a,b,c,d\] are proportional then they will have the same proportionality constant.
i.e.\[\dfrac{a}{b} = \dfrac{c}{d}\]
We will apply the same that is mentioned above 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 answer:
It is given that,\[\;x,15,36,27\] are in proportion to each other.
Since \[x,15,36,27\] are in proportion so we can write them as follows,
\[\dfrac{x}{{15}} = \dfrac{{36}}{{27}}\]
Let us now solve the above term by the method of cross multiplication,
That is let us multiply by 15 on both sides of the above given equation so that we get,
\[x = \dfrac{{15 \times 36}}{{27}}\]
On solving the terms in numerator and denominator we get,
\[x = \dfrac{{15 \times 4}}{3}\]
\[x = 5 \times 4\]
\[x = 20\]
 Hence we have found the value of\(x\) as 20.

Note:
If \[x,y,z\] are in proportion then\[\dfrac{x}{y} = \dfrac{y}{z}\] .
That is if three terms are said to be in proposition we get \[\dfrac{x}{y} = \dfrac{y}{z}\]
If \[a,b,c,d\] are proportional then they will have the same proportionality constant\[\dfrac{a}{b} = \dfrac{c}{d}\].
That is if four terms are in proportion then we get\[\dfrac{a}{b} = \dfrac{c}{d}\].
Here while solving the proportion we are just comparing the fractions on both sides of the equation whenever two fractions are said to be equal they both have the same values after the reduction.
That is we can say \[\dfrac{x}{{15}} = \dfrac{{36}}{{27}} = \dfrac{{12}}{9} = \dfrac{4}{3}\] that is we should get \[\dfrac{x}{{15}} = \dfrac{4}{5}\] on cross multiplying we get,
\[x = \dfrac{{4 \times 15}}{3} = 4 \times 5 = 20\], here the value of x is found easily.