Question

4. Represent the following as linear equations in two variables also draw a graph for the same. A farm raises cows and chickens. The farmer has a total of 42 animals. One day he counts the legs of all of his animals and realizes he has a total of 114. Solve graphically to find how many cows and chickens does the farmer have. Verify your solution using an algebraic method.

Answer 1

Answer:

COWS X 4 LEGS + CHICKENS X 2 LEGS = 114 LEGS TOTAL

COWS + CHICKENS = 42

COWS = 42 - CHICKENS

SUBSTITUTING BACK INTO THE FIRST EQUATION,

(42 - CHICKENS) X 4 LEGS + CHICKENS X 2 LEGS = 114

THIS SIMPLIFIES (AFTER MULTIPLICATION) INTO

168 - 4 X CHICKENS + 2 X CHICKENS = 114

OR

54 - 2 X CHICKENS = 0

54 = 2 X CHICKENS. THEN DIVIDING BOTH SIDES BY 2

54 / 2 = CHICKENS … OR 27 CHICKENS.

SINCE THERE ARE 27 CHICKENS, THE REST OF THE 42 MUST BE COWS.

42 - 27 = 15 COWS

A. THERE ARE 15 COWS, AND 27 CHICKENS