Question

Question #433bf

Answer 1

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