Twelve more than twice a certain number is six fewer than the three times the number. What is the number ?
(A) $ 6 $
(B) $ 12 $
(C) $ 16 $
(D) $ 18 $
Last updated date: 27th Mar 2023
•
Total views: 207k
•
Views today: 2.84k
Answer
207k+ views
Hint: In the given question, we are required to write an algebraic equation based on the information given to us. First, we break down the information given to us to try and identify what the algebraic equation must look like. You should always know what you are dealing with. A sum means that you are adding something, so you are going to use the $ + $ sign and so on. Then, after framing a mathematical equation, we try to solve it by using the method of transposition.
Complete step-by-step answer:
The statement “twelve more than twice a certain number” means first multiplying a number by $ 2 $ and then adding $ 12 $ to the product.
So, let us assume that the number is x.
Then, we get the algebraic expression $ \left( {2x + 12} \right) $ .
Now, we are given that the expression is six fewer than the three times the number assumed.
Now, we know that three times the number is $ 3x $ .
So, framing the mathematical equation, we get,
$ \Rightarrow \left( {2x + 12} \right) = \left( {3x - 6} \right) $
Now, we have to solve the above equation using the transpositions and simplification methods.
Shifting all the terms consisting x to the right side of the equation and all the constants to the left side, we get,
$ \Rightarrow 12 + 6 = 3x - 2x $
Simplifying the expression further, we get,
$ \Rightarrow x = 18 $
So, the value of x is $ 18 $ .
Hence, option (D) is correct.
So, the correct answer is “Option D”.
Note: An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division.
An equation will always use an equivalent $ \left( = \right) $ operator between the two terms. Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding value of the required parameter.
Complete step-by-step answer:
The statement “twelve more than twice a certain number” means first multiplying a number by $ 2 $ and then adding $ 12 $ to the product.
So, let us assume that the number is x.
Then, we get the algebraic expression $ \left( {2x + 12} \right) $ .
Now, we are given that the expression is six fewer than the three times the number assumed.
Now, we know that three times the number is $ 3x $ .
So, framing the mathematical equation, we get,
$ \Rightarrow \left( {2x + 12} \right) = \left( {3x - 6} \right) $
Now, we have to solve the above equation using the transpositions and simplification methods.
Shifting all the terms consisting x to the right side of the equation and all the constants to the left side, we get,
$ \Rightarrow 12 + 6 = 3x - 2x $
Simplifying the expression further, we get,
$ \Rightarrow x = 18 $
So, the value of x is $ 18 $ .
Hence, option (D) is correct.
So, the correct answer is “Option D”.
Note: An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division.
An equation will always use an equivalent $ \left( = \right) $ operator between the two terms. Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding value of the required parameter.
Recently Updated Pages
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

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

Tropic of Cancer passes through how many states? Name them.

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

Name the Largest and the Smallest Cell in the Human Body ?
