Question

If $y$ is directly proportional to $x$ and $y = 5$ when $x = 2$, what is the value of $y$ when $x = 16$?

Answer 1

To solve this question first we have to express the language in mathematical expression using the proportionality sign. Then we have to make an equation by removing the proportional sign and then put the value in that equation and find the value of k and put that in the original equation. Then put the value of x in order to get the value of y in the equation and solve that.

Complete step by step solution:
Given,
$y$ is directly proportional to $x$.
$y = 5$ when $x = 2$.
To find,
value of $y$ when $x = 16$.
First we express $y$ is directly proportional to $x$ in a mathematical expression.
So the mathematical expression is $y \propto x$.
Now on removing the proportionality sign and make equation we have to multiplying by a constant.
$y = kx$
Here k is constant.
Now we put $y = 5$ when $x = 2$ in the equation and find the value k.
$5 = k \times 2$
Now on rearranging we get the value of k.
$\dfrac{5}{2} = k$
Now putting the value of k in first equation-
$y = \dfrac{5}{2}x$
Now we have to find the value of y on $x = 16$
On putting this value in the equation.
$y = \dfrac{5}{2} \times 16$
On further calculations
$y = 8 \times 5$
$y = 40$
The value of y is 40 when $x = 16$ and satisfying all the conditions given in the question.
Note:
Although this question is easy, students must have a knowledge of proportionality and know what we have to add in order to remove the proportional sign and make that in the form of the equation. This is the only place where students often make mistakes.