Respuesta :
Answer:
36
Step-by-step explanation:
Here is the correct and complete question: The units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than twice the original number. What is the original number?
Lets assume the original number be"10y+x". (x is unit digit and y is 10th digit)
∴ if number is reversed then resulting number be "10x+y".
As given: x= 2y
and [tex]10x+y= 2(10y+x)-9[/tex]
Now, solving the equation to get original number.
[tex]10x+y= 2(10y+x)-9[/tex]
Distributing 2 to 10y and x, then opening the parenthesis.
⇒ [tex]10x+y= 20y+2x-9[/tex]
subtracting by (2x+y) on both side.
⇒ [tex]8x= 19y-9[/tex]
subtituting the value of "x", which is equal to 2y.
∴ [tex]8\times 2y= 19y-9[/tex]
⇒ [tex]16y=19y-9[/tex]
subtracting both side by (16y-9)
⇒ [tex]3y= 9[/tex]
cross multiplying
We get, [tex]y= 3[/tex]
y=3
∵x= 2y
[tex]x=2\times 3= 6[/tex]
∴ x= 6
Therefore, the original number will be 36 as x is the unit number and y as tenth number.
