Answer:
The original number = 72
Step-by-step explanation:
Let:
- the tens digit of the original number = x
- the ones digit of the original number = y
Then:
- the value of the original number = 10x + y
- the sum of the original number's digits = x + y
- the value of the reversed number = 10y + x
The statement "the sum of its digits is 1/8 of the number" can be written as:
[tex]x+y=\frac{1}{8} (10x+y)[/tex]
[tex]8(x+y)=10x+y[/tex]
[tex]10x-8x=8y-y[/tex]
[tex]\bf 2x=7y\ ...\ [1][/tex]
The statement "When the digits of the number are reversed and the number is subtracted from the original number, the result obtained is 45" (original number - reversed number = 45) can be written as:
[tex](10x+y)-(10y+x)=45[/tex]
[tex]9x-9y=45[/tex]
[tex]\bf x-y=5\ ...\ [2][/tex]
The system of equations will be:
[tex]\displaystyle\left \{ {{2x=7y} \atop {x-y=5}} \right.[/tex]
To solve the system of equations:
2x = 7y ⇔ 2x - 7y = 0
x - y = 5 ⇔ 2x - 2y = 10
-------------------- (-)
-5y = -10
y = 2
[2]
x - y = 5
x - 2 = 5
x = 7
Therefore, the original number = 72
