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# Find the value of $x$in the following proportion $5:15 = 4:x$

Last updated date: 18th Jun 2024
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Hint: A proportion is a mathematical comparison between two numbers. Often, these numbers can represent a comparison between things or people. For example, say you walked into a room full of people. You want to know how many boys there are in comparison to how many girls there are in the room. You would write that comparison in the form of a proportion.
A ratio is a way to compare two quantities by using division as in miles per hour.
A proportion on the other hand is an equation that says that two ratio are equivalent
If one number in a proportion is unknown you can find that number by solving the proportion
It is formulate as:
$a:b::c:d$
$\Rightarrow \dfrac{a}{b} = \dfrac{c}{d}$
$\Rightarrow a \times d = b \times c$
Therefore,

Given
$5:15 = 4:x......(1)$
We need to find the value of $x$in proportion.
We know that if two number are in proportion i.e $a:b::c:d$ or $a:b = c:d,$then we can write them as$\dfrac{a}{b} = \dfrac{c}{d}$
Hence $(1) \Rightarrow \dfrac{5}{{15}} = \dfrac{4}{x}$
Cross multiplying, we get
$5 \times x = 15 \times 4$
$\Rightarrow x = \dfrac{{15 \times 4}}{5}$
As 5 was in multiplication LHS it will be in division on RHS
$\Rightarrow x = 3 \times 4$
$\Rightarrow x = 12$
Hence the value of $x$ is 12.

Note: For four numbers a, b, c, d if $a:b = c:d$ then $b:a = d:c,$ it is known as invert and properly
For four numbers a ,b, c, d if $a:b = c:d$ then $a:c = b:d$if the second and third terms interchange their places, it is known as alternator property.
We can also use component do and dividend property to simply the proportion problems.