Answer:
original number: 27
reversed number: 72
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