Question

The product of two successive multiples of 4 is 28 more than the first multiple of 4. Find the multiples.

Answer 1

Given that, the product of two successive multiples of $4$ is $28$ more than the first multiple.

To find out: The multiples.

Let the multiples be $4x$ and $4x+4$

$\therefore 4x(4x+4)=28+4x$

$\Rightarrow 4x^2+4x-7-x=0$

$\Rightarrow 4x^2+3x-7=0$

$\Rightarrow 4x^2-4x+7x-7=0$

$\Rightarrow 4x(x-1)+7(x-1)=0$

$\Rightarrow (4x+7)(x-1)=0$

$\therefore x=\frac{-7}{4}$ or $x=1$

$x$ cannot be a negative number.

$\therefore x=1$

Hence, the multiples are $4$ and $8$.