Question 1170063
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<pre>

Let J be the number of card June had initially

    K be the number of card Kevin had initially.



The statement  "If june gives Kevin half her cards Kevin will have 72 more cards than june" means

    J - {{{J/2}}} = K + {{{J/2}}} - 72.     (1)

   +-----------------------------------+
   |   It is the LITERAL translation.  |
   +-----------------------------------+


From equation (1),  after multiplying both sides by 2

    2J - J = 2K + J - 144

    2J - J - J = 2K - 144

     0         = 2K - 144

   144         = 2K

     K         = 144/2 = 72.


Half of the problem is just solved.

Now start working on the second part.



The statement  "If June gives Kevin one sixth of her cards Kevin will have 16 less cards than June" means

    J - {{{J/6}}} = K + {{{J/6}}} + 16.     (2)

   +-----------------------------------+
   |   It is the LITERAL translation.  |
   +-----------------------------------+


From equation (2),  after multiplying both sides by 6


    6J - J = 6K + J + 96

    6J - J - J = 6K + 96

    4J         = 6K + 96

    4J         = 6*72 + 96

    4J         = 528

     J         = 528/4 = 132.


<U>ANSWER</U>.  Initially,  June had 132 cards;  Kevin had 72 cards.
</pre>

Solved.


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Do not accept any other answer.



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To see other similar solved problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Virtual-exchange-between-two-persons.lesson>Virtual exchange between two persons</A>

in this site.