SOLUTION: I am having a hard time figuring out how to write the equation for this problem: Joyce makes $6000 more per year than her husband does. Joyce saves 10% of her income for retirem

Question 69850: I am having a hard time figuring out how to write the equation for this problem:
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?
Found 2 solutions by checkley75, bucky:
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
Joyce's salary=x+6000
Husband's salary=x
10% of Joyce's salary plus 6% of her husband's salary which equals 5400.
.1(x+6000)+.06x=5400
.1x+600+.06x=5400
.16x=5400-600
.16x=4800
x=4800/.16
x=30000 which is hubby's salary.
thus Joyces salary is 30000+6000=36000
proof
.1*36000+.06*30000=5400
3600+1800=5400
5400=5400

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
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:

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

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
. Her husband saves 6% of his income or in decimal form he saves .
Added together, these two amounts of savings totals $5400. In equation form this becomes:

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

One way to do it is to multiply the entire bottom equation by -10 so that it becomes:

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

Calculator time. Divide both sides by -1.6 to get

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

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.
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