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Linear Equations In One Variable | Linear Equations In One Variable Exercise 8.4

Question 5

A man says, “I am thinking of a number. When I divide it by 3 and then add 5, my answer is twice the number I thought of”. Find the number.

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  • Solution

  • Transcript

Let the required number be x.

So, according to question:

⇒ x/3 + 5 = 2x

Transposing x/3 to RHS, we get

⇒ 5 = 2x – (x/3)

⇒ 5 = (6x – x)/3

⇒ 5 = (5x/3)

Multiplying both sides by 3 we get,

⇒ 5 × 3 = (5x/3) × 3

⇒ 15 = 5x

Dividing both sides by 5 we get

⇒ 15/5 = 5x/5

⇒ 3 = x

Thus the number thought of by the man is 3.

"Blahey kids how are you i hope everyone's fine so welcome to lido q a i'm vinit and i'm on lido tutor and we are here with another dose of mathematics for you okay so today what we are going to do today we are going to do this question on the board okay and solve it so this man okay he says i am thinking of a number when i divide it by 3 and then add 5 my answer is twice the number i thought of find the number so now this man is challenging you to find the number okay and he has given you hints what are the hints he says when he divides it by 3 and then adds 5 to the answer his answer is twice the number okay so these are the numbers of the number of the equation of the question okay yeah now what we are going to do what is the unknown here x we have to find the number so first of all okay right solution okay so let the number be x now what is it telling you he is telling you when he divides it by 3 so x divided by 3 and then add 5 to the question ok he gets twice the number yes my answer is means equal to twice the number now we have x here we have x on the right hand side so how do we solve equations when we have variables on both the sides simple we bring the variables on the same side and the numbers on the other side so we can write this as 5 equal to 2x and since we are transposing we perform the inverse operation so x by 3 right now these are unlike fractions the denominator here is 1 the lcm of these two are 3 the lcm here is 3 so what you do is you multiply the numerator and the denominator of 2x by 1 by 3 okay so when you multiply it what do you get 5 is equal to 6 x by 3 minus x by 3. so can we write okay now can we just interchange to bring it in our standard format variables on the left side and once the constant on the right side because we are used to that method so yeah let's do that because a plus b is equal to 5 is the same as 5 is equal to a plus b yeah doesn't matter if we change the size so 6x minus x by 3 is equal to 5 okay now we transpose this 3 to the right hand side and perform the inverse operation so this becomes 5x is equal to 5 into 3 that is 15 okay again we transpose this coefficient which is 5 and we take this to the right hand side and perform the inverse operation which will be division so x will be 15 by 5 which is equal to 3 so what is the number that the person was thinking it was it is 3 okay now we can tell him the answer right now let's check the answer to be sure right so if he divides three by three he gets one then he adds five to 8 he gets 6 yes now 6 is again equal to 2 into 3 3 is the number he thought of twice the number so it satisfies the conditions given by the man so yes x is equal to 3 is the answer so i hope this video helps you and i hope you enjoyed the video so don't forget to like the video if you enjoyed the video and if you have any doubts please leave a comment below also don't forget to subscribe to the channel because we keep coming up with these videos and you have to be the first one to be able to watch this video and excel in your mathematics okay bye guys nk"

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Question 5

A man says, “I am thinking of a number. When I divide it by 3 and then add 5, my answer is twice the number I thought of”. Find the number.

  • Solution

  • Transcript

Let the required number be x.

So, according to question:

⇒ x/3 + 5 = 2x

Transposing x/3 to RHS, we get

⇒ 5 = 2x – (x/3)

⇒ 5 = (6x – x)/3

⇒ 5 = (5x/3)

Multiplying both sides by 3 we get,

⇒ 5 × 3 = (5x/3) × 3

⇒ 15 = 5x

Dividing both sides by 5 we get

⇒ 15/5 = 5x/5

⇒ 3 = x

Thus the number thought of by the man is 3.

"Blahey kids how are you i hope everyone's fine so welcome to lido q a i'm vinit and i'm on lido tutor and we are here with another dose of mathematics for you okay so today what we are going to do today we are going to do this question on the board okay and solve it so this man okay he says i am thinking of a number when i divide it by 3 and then add 5 my answer is twice the number i thought of find the number so now this man is challenging you to find the number okay and he has given you hints what are the hints he says when he divides it by 3 and then adds 5 to the answer his answer is twice the number okay so these are the numbers of the number of the equation of the question okay yeah now what we are going to do what is the unknown here x we have to find the number so first of all okay right solution okay so let the number be x now what is it telling you he is telling you when he divides it by 3 so x divided by 3 and then add 5 to the question ok he gets twice the number yes my answer is means equal to twice the number now we have x here we have x on the right hand side so how do we solve equations when we have variables on both the sides simple we bring the variables on the same side and the numbers on the other side so we can write this as 5 equal to 2x and since we are transposing we perform the inverse operation so x by 3 right now these are unlike fractions the denominator here is 1 the lcm of these two are 3 the lcm here is 3 so what you do is you multiply the numerator and the denominator of 2x by 1 by 3 okay so when you multiply it what do you get 5 is equal to 6 x by 3 minus x by 3. so can we write okay now can we just interchange to bring it in our standard format variables on the left side and once the constant on the right side because we are used to that method so yeah let's do that because a plus b is equal to 5 is the same as 5 is equal to a plus b yeah doesn't matter if we change the size so 6x minus x by 3 is equal to 5 okay now we transpose this 3 to the right hand side and perform the inverse operation so this becomes 5x is equal to 5 into 3 that is 15 okay again we transpose this coefficient which is 5 and we take this to the right hand side and perform the inverse operation which will be division so x will be 15 by 5 which is equal to 3 so what is the number that the person was thinking it was it is 3 okay now we can tell him the answer right now let's check the answer to be sure right so if he divides three by three he gets one then he adds five to 8 he gets 6 yes now 6 is again equal to 2 into 3 3 is the number he thought of twice the number so it satisfies the conditions given by the man so yes x is equal to 3 is the answer so i hope this video helps you and i hope you enjoyed the video so don't forget to like the video if you enjoyed the video and if you have any doubts please leave a comment below also don't forget to subscribe to the channel because we keep coming up with these videos and you have to be the first one to be able to watch this video and excel in your mathematics okay bye guys nk"

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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