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If $\frac{3}{4}$ y = 6 − $\frac{1}{3}$ c, then the value of 2c + $\frac{9}{2}$ y is

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answer is C.

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Detailed Solution

Given,

\frac{3}{4}

y = 6 −

\frac{1}{3}

c………….. (1)
To find, 2c +

\frac{9}{2}

y…………. (2)
So from the above equation take

\frac{1}{3}

c from RHS to LHS of equation 1 we have,

\frac{1}{3}

c +

\frac{3}{4}

y = 6………… (3)
Now as we see that in the above equation the coefficient of c and y is

\frac{1}{3}

and

\frac{3}{4}

and in the equation whose value we have to find out the coefficient of c and y is 2 and

\frac{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.

\frac{1}{3}

and

\frac{3}{4}

of the given equation we get the same coefficients i.e. 2 and

\frac{9}{2}

.
So multiply by 6 in equation (3) we have,
⇒ 6 (

\frac{1}{3}

c +

\frac{3}{4}

y) = 6 (6)
⇒

\frac{6}{3}

c +

\frac{18}{4}

y = 36
⇒ 2c +

\frac{9}{2}

y = 36
Hence, option 3 is correct.

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