Maths Problems: Take One

Math problems: Basic Technical Mathematics with Calculus 5th Ed
Ch 1. Exercise 1-13

Q1. Two computers programs cost $390 dollars together.
If one costs $114 more than the other, what is the cost of each?

I was going to jump ahead on this one,
but I couldnt quite figure it out.
Anyway -- the statement of the problem gives us our hint

Two computer programs ...
we have two unknown numbers
so lets call them
a and b
a + b = 390
one costs $114 more than the other

a + 114 = b
or
b = a + 114
since b = a + 114 then we can replace b with a + 114

so we now have:
a + a + 114 = 390
which is the same as
2a + 114 = 390
we can move the 114 across to the right hand side of the equals and subtract it:
2a = 390 - 114
2a = 276
we can move the 2 across and divide it off 276
a = 276 / 2
so we can now calculate a:
a = 138
and we can get b because we know
b = a + 114
b = 252
so we can double check
a = 138
b = 252
-------
a + b = 390
138 + 252 = 390