Question

5. The sum of the digits of a two- digit number is 12. When the digits are reversed, the new number obtained is 15 more than twice the original number. Find the original number.

Answer 1

Dare I even start, or do you already have your answer? XD

Answer 2

i'm starting.. but i badly need a helping hand
:(

Answer 3

what numbers can equal 12?

Answer 4

single digit numbers*

Answer 5

3+9

Answer 6

Let's let x and y be the digits of your original number such that x is the tens digit.

then x + y = 12, yes?

Answer 7

cant be 39, 93 is more than 15 more

Answer 8

5+7?

Answer 9

Don't guess. We'll do this systematically... we know x + y = 12, now what other expression can we derive about x and y?

Answer 10

As for the numbers themselves, if x is the tens digit, then the first number is
10x + y, correct?

Answer 11

ya..

Answer 12

Now, if we reverse the digits, then the new number is 10y + x, yes?

Answer 13

Now this new number is \(\color{red}{\text{15 more than TWICE the original number}}\)

Answer 14

So, in maths terms this is
\[\Large 10y+x = 2[10x+y]+15\]

Answer 15

then we proceed... 10y + x = 20x + 2y + 15

Answer 16

Yes. Simplify that, and couple it with x+y = 12 to form a system, and then just solve it.

Answer 17

transposition will do?

Answer 18

Whatever method appeals to you :P

Answer 19

If you like, you can directly replace the x in that longer equation with 12-y, and then just solve for y.

Answer 20

10y + x = 20x + 2y + 15
substitute x
x=12-y
10y - (12 - y) = 20(12 - y) + 2y + 15
10y + y - 12 =240 + 20y +15
11y - 12 = 20y + 255
11y - 20y = 255+12
-9y = 267
y = -29.666666666

would be badly wrong or i'm just making it worst..

Answer 21

There's something amiss... hang on.

Answer 22

just consider the original number like xy where x is number on tens place and y on units place...now apply all the conditions on x and y and solve for them

Answer 23

A lot of mistakes, and they all stem from these two lines.
10y - (12 - y) = 20(12 - y) + 2y + 15
10y + y - 12 =240 + 20y +15

First of all, it was
10y + x = 20x + 2y + 15
So after replacing x with 12-y
you get
10y + (12 - y) + 20(12 - y) + 2y + 15
Why don't you work from here^ instead?

Answer 24

is it really 10y + (12 - y) + 20(12 - y) + 2y + 15
or it should be 10y + (12 - y) = 20(12 - y) + 2y + 15..

Answer 25

sorry, typo. Proceed

Answer 26

10y + 12 - y = 240 - 20y + 2y + 15
9y + 12 = 255 - 18y
9y + 18y = 255 - 12
27y = 243
y = 9

x = 12 - y
x = 12 - 9
x = 3

the number is 39

2(39) + 15 = 93 there thanks a lot master :D

Answer 27

Much better.