document.write( "Question 1205469: Mr. Choo had some blue and red stickers at first. If he gives out 4 blue stickers and 5 red stickers everyday, he will be left with 24 blue stickers and 0 red sticker. If he gives out 9 blue stickers and 4 red stickers everyday for the same number of days as before, he will be left with 1/3 as many red stickers as blue stickers. How many blue stickers did he have at first? \n" ); document.write( "

Algebra.Com's Answer #842293 by ikleyn(52799) $\"\"$ $\"About$

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\n" ); document.write( "Mr. Choo had some blue and red stickers at first.
\n" ); document.write( "(a) If he gives out 4 blue stickers and 5 red stickers everyday, he will be left with 24 blue stickers
\n" ); document.write( "and 0 red sticker.
\n" ); document.write( "(b) If he gives out 9 blue stickers and 4 red stickers everyday for the same number of days as before,
\n" ); document.write( "he will be left with 1/3 as many red stickers as blue stickers.
\n" ); document.write( "How many blue stickers did he have at first?
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document.write( "Let R be the number of red stickers;  B be the number of blue stickers and n be the number of days.\r\n" );
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document.write( "Then from statement (a) \r\n" );
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document.write( "    R = 5n        (1) \r\n" );
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document.write( "    B = 4n + 24.  (2)\r\n" );
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document.write( "From statement (b), after n days, the number of blue stickers will be       B-9n = (4n+24)-9n = 24-5n,\r\n" );
document.write( "                                  while the number of red stickers will be  5n-4n = n.\r\n" );
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document.write( "    \r\n" );
document.write( "Then, according to statement (b),  we have this equation for unknown \"n\"\r\n" );
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document.write( "    3n = 24-5n    (3)\r\n" );
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document.write( "From equation (3), we find\r\n" );
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document.write( "    3n + 5n = 24  --->  8n = 24  --->  n = 24/8 = 3  (days).\r\n" );
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document.write( "Hence, the number of blue stickers initially, according to formula (2), was \r\n" );
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document.write( "    B = 4n + 24 = 4*3 + 24 = 12 + 24 = 36.  \r\n" );
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document.write( "ANSWERE.  The number of blue stickers was 36 at first.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The strategy is as follows.\r
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document.write( "    (1)  Introduce n = the number of days.\r\n" );
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document.write( "    (2)  From the first statement, deduce expressions for red sticks and for blue sticks separately.\r\n" );
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document.write( "    (3)  From the second statement, deduce expressions for remaining sticks.\r\n" );
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document.write( "    (4)  Then from statement (b) make an equation and solve it for the number of days.\r\n" );
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document.write( "    (5)  Having the number of days, restore the unknown number of blue sticks.\r\n" );
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