SOLUTION: Hi June and Kevin have some cards. If june gives Kevin half her cards Kevin will have 72 more cards than june. If June gives Kevin one sixth of her cards Kevin will have 16 les

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Question 1170063: Hi
June and Kevin have some cards. If june gives Kevin half her cards Kevin will have 72 more cards than june. If June gives Kevin one sixth of her cards Kevin will have 16 less cards than June.
How many cards do they have.
Thanks
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
June and Kevin have some cards.
let’s say June have x cards and Kevin have y cards
if June gives Kevin half her cards Kevin will have 72 more cards than June
y-72=x-x%2F2
y=x%2F2%2B72....eq.1

if June gives Kevin one sixth of her cards Kevin will have 16 less cards than June

y%2B16=x-x%2F6
y=5x%2F6-16...eq.2

from eq.1 and eq.2 we have

x%2F2%2B72=5x%2F6-16......both sides multiply by 6
16%2B72=5x%2F6-x%2F2
88=5x%2F6-3x%2F6
88=2x%2F6
88=x%2F3
+x=88%2A3
+x=264

y=x%2F2%2B72....eq.1, substitute +x=168
y=264%2F2%2B72
y=132%2B72
y=204

June have 264 cards and Kevin have 204 cards

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

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%2F2 = K + J%2F2 - 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%2F6 = K + J%2F6 + 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.


ANSWER.  Initially,  June had 132 cards;  Kevin had 72 cards.

Solved.

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Do not accept any other answer.


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Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
June and Kevin have some cards. If june gives Kevin half her cards Kevin will have 72 more cards than june. If June gives Kevin one sixth of her cards Kevin will have 16 less cards than June.
How many cards do they have.
Thanks
Let original number of cards that Kevin and June had, be K, and J, respectively



When June gives Kevin ½ of her cards, she will have ½J left, and Kevin will have K + ½J  

We then get: K + ½J = ½J + 72

matrix%281%2C3%2C+K+%2B+%281%2F2%29J+-+%281%2F2%29J%2C+%22=%22%2C+72%29

Original number of cards that Kevin had, or highlight_green%28matrix%281%2C3%2C+K%2C+%22=%22%2C+72%29%29



When June gives Kevin 1%2F6 of her cards, she will have 5J%2F9 left, and Kevin will have K+%2B+J%2F6 cards  

We then get: 

Original number of cards that June had, or 

Any other answer is RIDICULOUS, WRONG, and RUBBISH, so ignore it!