If $$3x + 6y + 9z = \frac{20}{3}, 6x + 9y + 3z = \frac{17}{3}$$ and $$18x + 27y - z = \frac{113}{9}$$, then what is the value of $$75x + 113y$$?
$$3x+6y+9z=\frac{20}{3}.$$
or, $$x+2y+3z=\frac{20}{9}...............\left(1\right)$$
$$6x+9y+3z=\frac{17}{3}.$$
or, $$2x+3y+z=\frac{17}{9}................\left(2\right)$$
$$18x+27y-z=\frac{113}{9}.$$
or, $$72x+108y-4z=\frac{452}{9}.......................\left(3\right)$$
By adding (1),(2) & (3) :
$$75x+113y=\frac{452}{9}+\frac{20}{9}+\frac{17}{9}=\frac{489}{9}=\frac{163}{3}.$$
A is correct choice.
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