A number consists of rwo digit number whose sum is 9. If9 is subtracted from the number its digits are interchanged. Find the number
Your number = 10 a + b
a + b = 9
If 9 is subtracted from the number its digits are interchanged mean:
10 a + b - 9 = 10 b + a
Now:
10 a - 9 - a = 10 b - b
9 a - 9 = 9 b Divide both sides by 9
a - 1 = b
You must solve system:
a + b = 9
a - 1 = b
Try that.
The solutions are:
a = 5 , b = 4
Your number = 10 a + b = 10 ∙ 5 + 4 = 50 + 4 = 54
Proof:
5 + 4 = 9
54 - 9 = 45