Question #433bf

1 Answer
Nov 5, 2017

38

Explanation:

Let
x = ones digit
y = tens digit

the original number = 10y + x
the new number = 10x + y

We also know that:
x + y = 11
Rearranging,
x = 11 - y

The statement: "the new number is 45 more than the original number" can be mathematically written as:
10x+y = 10y + x + 45

Writing x in terms of y,
10(11-y)+y=10y+(11-y)+45
110-10y+y=10y+11-y+45
-10y+y-10y+y=-110+11+45
-18y=-54
y=3

x = 11 - y
x=11-3
x=8

Therefore, the original number is 38