Expert: Richard J. Raridon - 8/29/2009

Question
QUESTION: Hello:

I'm having difficulty solving the following. Perhaps you can help.

0.05x + 0.02y = 44
If I let x equal the following: x = 1000 - y and insert this into 0.05x + 0.02y = 44, I get 0.05(1000 - y) + 0.02y = 44.
50 - 0.05y + 0.02y = 44
This equals 50 - 0.03y = 44.

If I subtract 50 from both sides I get 0.03y = - 6
Does y equal -200 ?

I thank you for your reply.

ANSWER: With only one equation you cannot solve for two variables.  For any value of x there's a value for y and vice versa.  By stating that x = 1000-y, you created another equation.  If you have done your math correctly (should be -0.03y=-6), you would have gotten y=200 and therefore, x=800

---------- FOLLOW-UP ----------

QUESTION: Here are the two equations:

Equation 1. x + y = 1000, Solve for x. x = 1000 - y

Equation 2. 0.05x + 0.02y = 44

0.05(1000 - y) + 0.02y = 44

50 - 0.05y + 0.02y = 44

= 50 - 0.03y = 44

= -0.03y = 44 - 50

= -0.03y = -6

= -6/-0.03

= y = 200, if dividing two negative numbers equals a positive number.
It's been a long time since I have had algebra.

Is it possible to reverse engineer the above equation into something easier that uses basic arithmetic?  

Answer
You did use basic arithmetic. This time you put in a lot of extra steps that were not needed.  
The first time you had 50-0.03y = 44.  You then subtracted 50 from each side correctly but you lost the minus sign in front of 0.03y.  Yes, dividing two negative numbers gives you a positive number.  Multiplying two negative numbers also gives you a positive number.