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
<pre>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(1,3, K + (1/2)J - (1/2)J, "=", 72)}}}
Original number of cards that Kevin had, or {{{highlight_green(matrix(1,3, K, "=", 72))}}}

When June gives Kevin {{{1/6}}} of her cards, she will have {{{5J/9}}} left, and Kevin will have {{{K + J/6}}} cards  
We then get: {{{matrix(7,3, K + J/6, "=", 5J/6 - 16, K + J/6  -  5J/6, "=", - 16, K  -  4J/6, "=", - 16, 3K  -  2J, "=", - 48, 3(72)  -  2J, "=", - 48,  -  2J, "=", - 48  -  216,  -  2J, "=", - 264)}}}
Original number of cards that June had, or {{{highlight_green(matrix(1,5, J, "=", (- 264)/(- 2), "=", 132))}}}
Any other answer is RIDICULOUS, WRONG, and RUBBISH, so ignore it!