Question

The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed. Find the original number.

I got:
{t+u=8
10t+u=3(10u+t)+16
But I don't know how to solve it? And is it right?

Answer 1

62

Answer 2

how did you solve it

Answer 3

take this number as ab, so a+b=8 and (ab)+16=3(ba) which means 10a+b+16 =3(10b+a) If you solve the equation, you get 29b-7a=16 adn you know that a+b=8, if you solve them both, you get 36b=72 so b=2 and a=6 ab=62

Answer 4

wait what?

Answer 5

how is it (ab)+16=3(ba)?

Answer 6

The mistake you make is this: You should think that if you add 16 to the number, you get 3 times of this so 16 should be on the leftside

Answer 7

shouldn't it be 3(ab)+16

Answer 8

got it_?

Answer 9

no

Answer 10

how is (ab)+16=3(ba)?

Answer 11

The problem says " If 16 is added to the original number, the result is 3 times the original number with its digits reversed" which means if you add 16 to (ab), you get 3 times of(ba)

Answer 12

oh ok

Answer 13

i don't know you got 62

Answer 14

is it wrong?

Answer 15

when i solved 10a+b+16 =3(10b+a) I got 10a+16=29b+3a

Answer 16

no wait i got 7a+16=29b and i don't know what to do from there

Answer 17

10a+b+16=30b+3a so b+16=30b-7a and 29b-7a=16

Answer 18

shouldn't u subtract 3t though

Answer 19

ok now you geot the true equation 7a+16=29b... you know that a+b=8, for it is in the question.Now write these equations in two lines and solve them both

Answer 20

ok forget a and b..let's do it your way.. let the number be (ut).. you know that u+t=8 and 10u+t+16=3(10t+u)

Answer 21

10u+t+16=30t+3u so 7u-29t=-16 so 29t-7u=16

Answer 22

yea..

Answer 23

29t-7u=16 and u+t=8 so u=8-t. if you put 8-t in the first equation; 29t-7(8-t)=16 so 29t-56+7t=16 and t=2 here so u=6

Answer 24

so if t=2 and u=6, how do you know to put it 62? like how do you know to not put it as 26?

Answer 25

because in the beginning you named the number as (ut) which means u=6 and t=2 and ut is 62.. we solved it according to this information we put 10u instead of u so it is 62

Answer 26

o ok thanks so much

Answer 27

ur welcome:)