document.write( "Question 1210446: A basket contains k red and 7 green apples, where k is a constant. Two apples are picked randomly from the basket, one after the other without replacement. If the probability of picking two green apples is 7/12, find the:
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Algebra.Com's Answer #852557 by ikleyn(53354) $\"\"$ $\"About$

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\n" ); document.write( "A basket contains k red and 7 green apples, where k is a constant. Two apples are picked randomly from the basket,
\n" ); document.write( "one after the other without replacement. If the probability of picking two green apples is 7/12, find the:
\n" ); document.write( "(a) number of red apples in the basket
\n" ); document.write( "(b) total number of apples in the basket
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document.write( "Formula for the probability is  P = ,\r\n" );
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document.write( "so we have this equation\r\n" );
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document.write( "    \r\n" );
document.write( "     = .\r\n" );
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document.write( "Cancel common factor 7 in both sides.  You will get\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Cross-multiply to get\r\n" );
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document.write( "    (k+7)*(k+6) = 72.\r\n" );
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document.write( "Now you have the product of two consecutive integer numbers in the left side,\r\n" );
document.write( "and this product equals 72.\r\n" );
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document.write( "For anyone who knows the multiplication table, it is clear that the product is 8*9 = 72,\r\n" );
document.write( "so the lesser factor is 8\r\n" );
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document.write( "    k+6 = 8,\r\n" );
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document.write( "    k = 8-6 =2.\r\n" );
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document.write( "ANSWER.  (a) the number of green apples in the basket originally is 2;.\r\n" );
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document.write( "         (b) the total number of apples in the basket originally is 7+2 = 9.\r\n" );
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