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The Repeated Variable Concept

The Repeated Variable Concept is derived from the Comparison Concept and the Part-Whole Concept . This concept is applicable when the problem deals with one or more variables that is repeated, i.e., it is related to more than 1 variable in the question. For example, A is 1/2 of B and B is 2/3 of C. Thus B is the repeated variable.

To illustrate this concept, consider the following question.

Jane has 3 times as much money as Cindy. Lea has twice as much money as Jane. If Lea has $30 more than Cindy, how much money does Jane have?

Answer: Take note that Jane is the repeated variable,i.e., she is related to Cindy and then to Lea.

Step 1: Draw 1 box to represent Cindy's money and 3 boxes to represent Jane's money.

$repeated-variable-concept-001$

Step 2: Since Lea has twice as much as Jane, we draw twice as many number of units as Jane to represent Lea's money,i.e., 2 x 3 units = 6 units.

$repeated-variable-concept-002$

Step 3: From the question, we know that Lea has $30 more than Cindy. Since Lea has 5 units more than Cindy, then 5 units must be equal to $30.

$repeated-variable-concept-003$

5 units -----------> $30

1 unit ------------> $30 / 5 units = $6

3 units -----------> 3 units X $6 = $18

Therefore, Jane has $18.

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