The product of two successive integral multiples of 5 is 300. Determine the multiples.

Given:

The product of two successive integral multiples of 5 is 300.

 To do:

We have to find the multiples.

Solution:

Let the two successive integral multiples of $5$ be $5x$ and $5x+5$.

According to the question,

$(5x)(5x+5)=300$

$25x^2+25x=300$

$25x^2+25x-300=0$

$25(x^2+x-12)=0$

Solving for $x$ by factorization method, we get,

$x^2+x-12=0$

$x^2+4x-3x-12=0$

$x(x+4)-3(x+4)=0$

$(x+4)(x-3)=0$

$x+4=0$ or $x-3=0$

$x=-4$ or $x=3$

For $x=-4$,

$5x=5(-4)=-20$ and $5x+5=-20+5=-15$

For $x=3$,

$5x=5(3)=15$ and $5x+5=15+5=20$

Therefore, the two successive integral multiples of $5$ are $15$ and $20$ or $-15$ and $-20$ respectively. 

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Updated on: 10-Oct-2022

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