Random Maths Question of the Week!

[Nexus]

So today, I shall be starting to post a new maths question every week or so, and you guys will have to try to answer them! :3
Rules:
1. No cheating, please. And don't blatantly copy of someone else's answer.
2. Show your working out and make sure that you have covered all guidelines of the question.
3. The first person to get the answer right gets a "winner" rating <3
4. If you have any inquires, ask in the comments below. Answers will be revealed at the end of the week, if no one gets the answer correct.

Well, here's the first question:

1. The digits of a two digit number sum to 10. If the digits swap places the number is 36 more than the original number. What is the original number? Can you show an algebraic solution?
   
   
   Good luck and have fun!

 

[Duke_]

37 = 3 + 7 = 10. Switch them, you get 73. 73 - 36 = 37.

 

[Nexus]

37 = 3 + 7 = 10. Switch them, you get 73. 73 - 36 = 37.

Please show an algebraic solution :3

 

[ElectricShrew65]

Alright, here we go. (big numbers after letters symbolize powers)
1. Find the HCF:
2a (3+x) + 3d (3+x)
and
8a2 + 16a + 24a3
2. 9+10?

 

[Nexus]

Alright, here we go. (big numbers after letters symbolize powers)
1. Find the HCF:
2a (3+x) + 3d (3+x)
and
8a2 + 16a + 24a3
2. 9+10?

Could you please reiterate xD
Also, put down what each letter symbolises
eg. x is the first digit or y is the second digit and so on.

 

[Duke_]

Technically it said CAN you show an algebraic solution, it didn't say we had to.

 

[Nexus]

Technically it said CAN you show an algebraic solution, it didn't say we had to.

2nd rule states that you have to cover all question guidelines xD
And yes it is possible with algebra. So I want you to show me how :3

 

[█►тєяму◄█]

I bet this is her math summer work and this is her way of getting answers.

 

[Nexus]

I bet this is her math summer work and this is her way of getting answers.

Oh, it's winter where I am xD
And I don't have holidays at the moment,
And I do know the answer :3

 

[Azhiaziam707]

X=1st digit Y=2nd (answer being XY)
Given: X+Y=10 (X&Y must be 1-9)
Y"X-X"Y=36 ( I'm using "s to indicate just digits vs a product of the two)
So, Y"X - 36 = X"Y
written in power of 10s notation:
10Y+X -36 = 10X+Y ==>
(10Y-Y)+(X-10X)-36=0 ===>
9Y+(-9X)=36 ===> 9(Y-X)=36
So, Y-X=36/9 = 4
Giving Y-X=4 ==> Y=4+X
Then, using X+Y=10:
X+4+X=10 ===> 2X=6 ===> X=3
Plugging back in, Y=4+3 = 7
So X"Y= 37.
I understand I showed alot of redundant steps and calculations, but I didn't want to get marked down for not showing the work ;)

 

[Nexus]

X=1st digit Y=2nd (answer being XY)
Given: X+Y=10 (X&Y must be 1-9)
Y"X-X"Y=36 ( I'm using "s to indicate just digits vs a product of the two)
So, Y"X - 36 = X"Y
written in power of 10s notation:
10Y+X -36 = 10X+Y ==>
(10Y-Y)+(X-10X)-36=0 ===>
9Y+(-9X)=36 ===> 9(Y-X)=36
So, Y-X=36/9 = 4
Giving Y-X=4 ==> Y=4+X
Then, using X+Y=10:
X+4+X=10 ===> 2X=6 ===> X=3
Plugging back in, Y=4+3 = 7
So X"Y= 37.
I understand I showed alot of redundant steps and calculations, but I didn't want to get marked down for not showing the work ;)

Eyy we have a winner! :3
Good job, most people wouldn't be able to put it into algebraic terms, but it seems you have done it!

Congrats Azhia!


Also on a side note, I don't think I'll be adding anymore questions xD

 

[Azhiaziam707]

Eyy we have a winner! :3
Good job, most people wouldn't be able to put it into algebraic terms, but it seems you have done it!

Congrats Azhia!


Also on a side note, I don't think I'll be adding anymore questions xD

Yea it didn't seem to garner much interest on here. Thanks for the refresher on those though. I had solved one for an assignment before but it was a 3 digit problem, same concept.