Algebra problem

Question

Linda has twice as many chickens as she has ducks. After she sells 272 chickens and 16 ducks, she is left with half as many chickens as ducks. How many chickens did she have in the beginning?

Answer 1

Lets call her original amounts of chickens C and ducks D.

 

The first sentence says that C = 2D.

Then after she does her selling we have that  C - 272 = .5(D - 16) 

 

So we have a system of equations which can be solved by substitution.  Since C = 2D, we can plug the 2D in for C in the second equation and get a single equation with a single variable (ducks).  Solving this equation will tell us how many ducks she had at the beginning.  Multiplying that by 2 will tell us the original number of chickens.

 

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