Answer:
46
Step-by-step explanation:
Let
represent a number with
in the ten's position and
is the one's position.
This means
actually has value of
.
We are given the sum of those digits of
is 10; this means
.
It says if 18 is added to the number
, then the result is
.
So
has value
and
has value
.
We are given then:


Subtract
on both sides:

Simplify:

Subtract
on both sides:


Divide both sides by 9:

Rearrange by commutative property:

So the system of equations we want to solve is:


-------------------------Add equations together (this will eliminate the variable
and allow you to go ahead and solve for
:


Divide both sides by 2:

Simplify:

If
and
, then
.
since 4+6=10.
So the original number is (46).
18 more than 46 is 18+46=(64) which is what we wanted.
We also have the sum of 4 and 6 is 10 as well.