Question

Find two consecutive multiple of 3 whose product is 270.

Answer 1

Let the two consecutive multiples of $3$ be $3x$ and $3x+3$

Given that their product$=270$

$\Rightarrow 3x(3x+3)=270$

$\Rightarrow 9x(x+1)=270$

$\Rightarrow x(x+1)=30$

$\Rightarrow x^2+x-30=0$

$\Rightarrow x^2+6x-5x-30=0$

$\Rightarrow x(x+6)-5(x+6)=0$

$\Rightarrow (x+6)(x-5)=0$

$\Rightarrow x=-6,5$

Considering the positive value of $x$

$\Rightarrow x=5,3x=3\times 5=15$ and $3x+3=15+3=18$

$\therefore$ The two consecutive multiples of $3$ are $15$ and $18$