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

Last updated date: 19th Mar 2023

•

Total views: 304.5k

•

Views today: 7.84k

Answer

Verified

304.5k+ views

Hint – In this question the condition on multiples of 4 is given to us. So a multiple of 4 can be written as 4x where x belongs to positive integers and the successive multiple of 4 will be 4x+4 where x belongs to positive integers, so use this concept to get the answer.

“Complete step-by-step answer:”

It is given that the numbers are successive multiples of 4.

So, let the numbers be $4x$ and $\left( {4x + 4} \right)$.

Now it is given that the product of two successive multiples of 4 is 28 more than the first multiple of 4.

So, construct the linear equation according to this information we have,

Product of $4x$ and $\left( {4x + 4} \right)$ is equal to 28 plus $4x$.

$ \Rightarrow 4x\left( {4x + 4} \right) = 28 + 4x$

Now simplify the above equation we have,

$ \Rightarrow 16{x^2} + 16x = 28 + 4x$

$ \Rightarrow 16{x^2} + 12x - 28 = 0$

Now divide by 4 in above equation we have,

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

Now factories the above equation we have,

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

$

\Rightarrow x\left( {4x + 7} \right) - 1\left( {4x + 7} \right) = 0 \\

\Rightarrow \left( {x - 1} \right)\left( {4x + 7} \right) = 0 \\

\Rightarrow x - 1 = 0,{\text{ }}\left( {4x + 7} \right) = 0 \\

\Rightarrow x = 1,\dfrac{{ - 7}}{4} \\

$

Therefore the multiples is

$

4x = 4, - 7 \\

4x + 4 = 8, - 3 \\

$

Hence the multiples are (4 and 8) or (-7 and -3).

So this is the required multiples.

Note – Whenever we face such types of problems the key concept is simply to assume the multiple of 4 and then to write the consecutive multiple of 4. Now using the relevant relations provided in the questions and using the information equations can be formulated. Use these equations to get the right answer.

“Complete step-by-step answer:”

It is given that the numbers are successive multiples of 4.

So, let the numbers be $4x$ and $\left( {4x + 4} \right)$.

Now it is given that the product of two successive multiples of 4 is 28 more than the first multiple of 4.

So, construct the linear equation according to this information we have,

Product of $4x$ and $\left( {4x + 4} \right)$ is equal to 28 plus $4x$.

$ \Rightarrow 4x\left( {4x + 4} \right) = 28 + 4x$

Now simplify the above equation we have,

$ \Rightarrow 16{x^2} + 16x = 28 + 4x$

$ \Rightarrow 16{x^2} + 12x - 28 = 0$

Now divide by 4 in above equation we have,

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

Now factories the above equation we have,

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

$

\Rightarrow x\left( {4x + 7} \right) - 1\left( {4x + 7} \right) = 0 \\

\Rightarrow \left( {x - 1} \right)\left( {4x + 7} \right) = 0 \\

\Rightarrow x - 1 = 0,{\text{ }}\left( {4x + 7} \right) = 0 \\

\Rightarrow x = 1,\dfrac{{ - 7}}{4} \\

$

Therefore the multiples is

$

4x = 4, - 7 \\

4x + 4 = 8, - 3 \\

$

Hence the multiples are (4 and 8) or (-7 and -3).

So this is the required multiples.

Note – Whenever we face such types of problems the key concept is simply to assume the multiple of 4 and then to write the consecutive multiple of 4. Now using the relevant relations provided in the questions and using the information equations can be formulated. Use these equations to get the right answer.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE