SOLUTION: Hi Mrs Lee bought 20 ducks and chickens for 126 dollars. Each chicken cost 2 dollars less than each duck. If she bought 6 more chickens than ducks how much did she pay for each ch

I will solve the problem in two steps.


In  STEP 1,  I will determine the number of chickens (x) and ducks (y).

For it, I write two equations from the condition


    x + y = 20      (1)    (total)

    x - y =  6      (2)    (the difference).


To find x, add two equations


    2x = 26  ---->  x = 26/2 = 13.


Then from equation (2),  y = 20-x = 20-13 = 7.


So, 13 chicken and 7 ducs were bought.




Now in  STEP 2,  I will solve for the price of each chicken (p).


For it, I write the total money equation


    13p + 7*(p+2) = 126.


From this equation


    13p + 7p + 14 = 126

    20p = 126 - 14 = 112.


From this equation,   p = 112/20 = 5  dollars = 5   dollars = 5.60 dollars = 5 dollars and 60 cents.    ANSWER

Let number of chickens purchased, be C
Then number of ducks purchased = 20 - C
It was given that 6 more chickens than ducks were purchased
Therefore, the number of ducks purchased = C - 6 
We then get: 20 - C = C - 6
- C - C = - 6 - 20
- 2C =  - 26
Number of chickens purchased, or, 
Then number of ducks purchased = 20 - 13 = 7

Let cost of each chicken, be P
Then cost of each duck = P + 2
As $126 was spent, we get: 13P + 7(P + 2) = 126
13P + 7P + 14 = 126
20P = 112
Cost of a chicken, or,