Question 69850
Joyce makes $6000 more per year than her husband does. Joyce saves 10% of her income for retirement and her husband saves 6%. If altogether they save $5400 per year, then how much does each of them earn per year?

Suppose we let H represent the amount that her husband earns in a year and J represent the
amount that Joyce earns.

The first sentence tells you that J is $6000 more than H.  So if we take away $6000 from
J the amount left should be H.  In equation form this is:

{{{J - $6000 = H}}}

For later convenience, let's rearrange that by first adding $6000 to both sides and then
subtracting H from both sides to get:

{{{J - H = $6000}}}

Now let's look at the second part of the information given in the problem.

Joyce saves 10% of her income.  That is she saves 10% of J or in decimal form she saves
{{{0.1J}}}.  Her husband saves 6% of his income or in decimal form he saves {{{0.06H}}}.
Added together, these two amounts of savings totals $5400.  In equation form this becomes:

{{{0.1J + 0.06H = $5400}}}

You now have 2 linear equations that can be solved simultaneously:

{{{J - H = $6000}}} and
{{{0.1J + 0.06H = $5400}}}

One way to do it is to multiply the entire bottom equation by -10 so that it becomes:
{{{-J - 0.6H = -$54000}}}

If you add this equation to the first equation, the J and the -J cancel and the resulting
equation becomes:

{{{ -1.6H = -$48000}}}

Calculator time.  Divide both sides by -1.6 to get 

{{{ H = $30000}}}

And since Joyce makes $6000 more than that, you know she makes:

{{{J = $36000}}}

Check by seeing if 10% of Joyce's salary plus 6% of her husband's salary adds up to be $5400.

Hope this helps you to see that problems of this sort require 2 equations to solve, and
that they must be solved as simultaneous linear equations.