Question

Y varies directly with x,$y = 65$when $x = 5$.How do you find y when $x = 12$?

Answer 1

Hint:In order to determine the value of $y$when $x = 12$,express the relation between $x\,and\,y$as $y \propto x$which can be resolved into$y = kx$.determine the value of k by putting$x = 5$and$y = 65$and then put$x = 12$in the expression to find the value of $y$.

Complete step by step solution:
In order to write any mathematical expression from some words and figures, we must first find the relationship and the quantities specified. Here in this question the relation between $y$ and $x$ is that it's saying that $y$ varies directly with $x$.

Here, directly means that when the value of $x$increases the of $y$ also increases So we are replacing the ‘directly varies’ word from the sentence with the Proportional
symbol $y \propto x$

Resolving the proportionality symbol with the inclusion of proportionality constant$k$on the right- hand side

$y = kx$where k is the proportionality constant ---(1)

According to question, when$x = 5$ then $y = 65$so putting values of $x$ and $y$ in above
expression

$
65 = k(5) \\
\Rightarrow k = \dfrac{{65}}{5} \\
\Rightarrow k = 13 \\
$

Hence, the value of proportionality constant $k = 13$.

Let’s find out the value of $y$ when $x = 12$by putting the $x = 12$and $k = 13$in equation(1)
$
y = kx \\
y = (13)(12) \\
y = 156 \\
$

Therefore, the value of $y$when $x = 12$is equal to $156$.

Additional Information: 1.Mathematical equation: A Mathematical equation can be defined as the mathematical statement which contains an equal symbol $ = $ in between two algebraic expressions that share the same value. A algebraic expression can contain any number of variables generally we take 2-3 variables

Let assume a expression
$5x + 9 = 24$

It is a mathematical equation having LHS (Left-Hand-Side) equal to RHS (Right-Hand-Side)

Where $x$ is the variable 5 is the coefficient of variable $x$

And $24,9$are the constants

2.$2x + 98 + 78y$is not a mathematical equation because it does not contain equality $ = $ symbol .

It is only a mathematical expression.

Note: 1. Read the statement carefully in order to convert them into mathematical expressions.

2.If the relation between $x$and $y$is inversely proportional when the expression will be
$
y \propto \dfrac{1}{x} \\
y = (k)\dfrac{1}{x} \\
$

Where k is the proportionality constant.