document.write( "Question 1185489: Hi
\n" ); document.write( "Arthur and Sam shared some cards. If Arthur gave 20 to Sam they would have the same number of cards.
\n" ); document.write( "If Sam gave Arthur 10 cards the ratio of cards Arthur had to Sam is 2 to 1. How many cards did Arthur have at the end.\r
\n" ); document.write( "\n" ); document.write( "My sons answer is 110 the textbook is 120.\r
\n" ); document.write( "\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #816327 by MathTherapy(10552) $\"\"$ $\"About$

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Hi
\n" ); document.write( "Arthur and Sam shared some cards. If Arthur gave 20 to Sam they would have the same number of cards. If Sam gave Arthur 10 cards the ratio of cards Arthur had to Sam is 2 to 1. How many cards did Arthur have at the end.\r
\n" ); document.write( "\n" ); document.write( "My sons answer is 110 the textbook is 120.\r
\n" ); document.write( "\n" ); document.write( "Thanks
\n" ); document.write( "

The statement of the problem is AMBIGUOUS!\r\n" );
document.write( "If it's CONTINUOUS, then Arthur will have 40 cards at the end.\r\n" );
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document.write( "However, the number at the end is 120, if it's NOT CONTINUOUS and the problem is written as follows:  Arthur and Sam shared some cards. If Arthur\r\n" );
document.write( "gave 20 to Sam they would have the same number of cards. HOWEVER, if Sam gave Arthur 10 cards the ratio of cards Arthur had to Sam is 2 to 1. \r\n" );
document.write( "How many cards did Arthur have at FIRST. the end.\r\n" );
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document.write( "The \"110\" cards for Arthur at the end, that your son got, was actually what Arthur started with, not what he would've ended up with. At the same time,\r\n" );
document.write( "Sam started with 70 cards. \r\n" );
document.write( "When you SUBTRACT the 20 that Arthur gave Sam, from the 110 he started with, Arthur would've then ended up with 110 - 20 = 90. At the same time, Sam's 70\r\n" );
document.write( "cards would've become 70 + 20 = 90. As seen they both would've had the same number of cards (90) after this exchange.\r\n" );
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document.write( "However, when you ADD the 10 that Arthur would've received from Sam, to the 110 he started with, Arthur would've ended up with 110 + 10 = \r\n" );
document.write( "120 (The answer to the problem). At the same time, after giving Arthur 10 cards, Sam's 70 cards would've become 70 - 10 = 60. \r\n" );
document.write( "As seen directly above, Arthur's count of 120 to Sam's count of 60 would've yielded a \r\n" );
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document.write( "So, Arthur ends up with 90 if 1st scenario is applied, and with 120 if the 2nd one is! Therefore, the correct question should be how many he STARTED with,\r\n" );
document.write( "since that number never changes, regardless of the number of exchanges.

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