The Excess Value Concept

The Excess Value Concept is derived from a combination of the

Part-Whole Concept , the Comparison Concept and the Change Concept . A classic example of a question involving the Excess Value Concept is the "Chicken & Rabbit Legs" question. In these types of questions, both variables have a set of common values attached to them while one of the variables has an extra set of values attached to it. The idea is to isolate this extra set of excess value so that it could be subtracted from the total value of the two variables, thereby allowing us to divide the remaining unknown units equally to solve for its value.

To illustrate this concept, consider the following problem.

A farmer has 36 animals on his farm. They are either chickens or rabbits. Altogether, the chickens and rabbits have 100 legs. How many chickens are there?

Answer:



Step 1: First, let's assume all the animals on the farm are chickens. Each animal would have 2 legs. Draw a box to represent 1 animal with 2 legs.

excess-value-concept-001


Step 2: Draw an arrow to the right to show that this box is repeated 36 times (label "36" at the end of the arrow).

excess-value-concept-002


Step 3: Since all the animals have only 2 legs.

excess-value-concept-003


36 animals X 2 legs = 72 legs

Thus, they have a total of 72 legs (if they are all chickens).



Step 4: Since there are 100 legs in reality, the extra legs must belong to the rabbits(rabbits have 4 legs instead of 2). So, let's draw another long box to the right to represent the extra legs.

excess-value-concept-004


100 legs - 72 legs = 28 legs

Hence, there are 28 "extra legs".



Step 5: Since the legs belong to the rabbits, each rabbit should get 2 extra legs each.

excess-value-concept-005


28 extra legs / 2 legs per rabbit = 14 rabbits

36 animals - 14 rabbits = 22 chickens

Therefore, there are 22 chickens.






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