Question

If $\dfrac{3}{4}y = 6 - \dfrac{1}{3}c$, then the value of $2c + \dfrac{9}{2}y$ is
$\left( a \right)63$
$\left( b \right)24$
$\left( c \right)36$
$\left( d \right)42$

Answer 1

Hint: In this particular question use the concept that check the coefficients of c and y of the given equation and the equation whose value which we have to find out so multiply the coefficient of given equation in such a way that it is equal to the coefficients of asked equation, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given equation
$\dfrac{3}{4}y = 6 - \dfrac{1}{3}c$.................... (1)
Now we have to find the value of
$2c + \dfrac{9}{2}y$................... (2)
Now first simplify the equation (1) we have,
$ \Rightarrow \dfrac{3}{4}y = 6 - \dfrac{1}{3}c$
So from the above equation take $\dfrac{1}{3}c$ from RHS to LHS of the above equation we have,
$ \Rightarrow \dfrac{1}{3}c + \dfrac{3}{4}y = 6$..................... (3)
Now as we see that in the above equation the coefficient of c and y is $\dfrac{1}{3}{\text{ and }}\dfrac{3}{4}$ and in the equation whose value we have to find out the coefficient of c and y is ${\text{2 and }}\dfrac{9}{2}$ so multiply the coefficient of given equation in such a way that it is equal to the coefficients of asked equation.
So as we see that if we multiply by 6 in the coefficient of c and y i.e. $\dfrac{1}{3}{\text{ and }}\dfrac{3}{4}$ of the given equation we get the same coefficients i.e. ${\text{2 and }}\dfrac{9}{2}$.
So multiply by 6 in equation (3) we have,
$ \Rightarrow 6\left( {\dfrac{1}{3}c + \dfrac{3}{4}y} \right) = 6\left( 6 \right)$
$ \Rightarrow \dfrac{6}{3}c + \dfrac{{18}}{4}y = 36$
$ \Rightarrow 2c + \dfrac{9}{2}y = 36$
So the above equation is the same as equation (2).
So this is the required answer.
Hence option (c) is the correct answer.

Note: Whenever we face such types of questions check the coefficient of the variables in the given equations so just multiply those coefficients with a particular number as above so that we get the coefficients of the variable of the asked equation, then simplify we will get the required answer.