Respuesta :
Answer:
original number: 27
reversed number: 72
Step-by-step explanation:
Let the tens place digit = a
Let the units place digit = b
⇒ Original two-digit number = 10a + b
⇒ Reversed two-digit number = 10b + a
If the reversed two-digit number is 9 less than 3 times the original number:
⇒ 10b + a = 3(10a + b) - 9
⇒ 10b + a = 30a + 3b - 9
⇒ 7b = 29a - 9
If the different of the two numbers is 45 (and the reversed number is larger than the original number):
⇒ (10b + a) - (10a + b) = 45
⇒ 10b + a - 10a - b = 45
⇒ 9b -9a= 45
⇒ 9(b - a)= 45
⇒ b - a= 5
⇒ b = 5 + a
Substitute b = 5 + a into 7b = 29a - 9 and solve for a:
⇒ 7(5 + a) = 29a - 9
⇒ 35 + 7a = 29a - 9
⇒ 44 = 22a
⇒ a = 2
Finally, substitute the found value of a into b = 5 + a and solve for b:
⇒ b = 5 + 2 = 7
Therefore,
- original number: 27
- reversed number: 72
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To find :-
The original number
Given :-
The reverse of 2 digit number is 9 less than 3 times the original number
let tens digit of original number = x
ones digit = y
which means
(10y + x) + 9= 3(10x + y)
And the difference between the reverse digit and the original number is 45
(10y + x) - (10x + y) = 45
Solution :-
(10y + x) + 9 = 3(10x + y) ---------- {equation 1}
10y + x + 9 = 30x + 3y
9 = 30x - x + 3y - 10y
9 = 29x - 7y ---------- {equation 2}
(10y + x) - (10x + y) = 45 ---------- {equation 3}
10y - y - 10x + x = 45
9y - 9x = 45 (dividing whole equation by 9)
y - x = 5
y = 5 + x ---------- {equation 4}
(putting values of equation 4 in equation 2)
[tex]9 = 29x - 7(5 + x) \\ 9 = 29x - 35 - 7x \\ 9 + 35 = 29x - 7x \\ 44 = 22x \\ \frac{44}{22} = x \\ 2 = x[/tex]
(Putting the value of x in equation 4)
y = 5 + 2 = 7
Verification :-
(Taking equation 3 and putting values of x and y)
(10y + x) - (10x + y) = 45
(10×7 + 2) - (10×2 + 7) = 45
(70 + 2) - (20 + 7) = 45
72 - 27 = 45
45 = 45
- Hence, verified.
Result :-
The original number is 27.
