document.write( "Question 1100144: Mary Jo spends $2,860 to buy stock in two companies. She pays $13 a share to one of the companies and $26 a share to the other. If she ends up with a total of 150 shares, how many shares did she buy at $13 a share and how many did she buy at $26 a share? \n" ); document.write( "
Algebra.Com's Answer #714628 by ikleyn(52865)\"\" \"About 
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\n" ); document.write( "        There are different methods to solve the problem.
\n" ); document.write( "        I will show you 3 (three) basic methods in this post.\r
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\n" ); document.write( "\n" ); document.write( "Solution 1   (the system of  2  equations approach)\r
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document.write( "Let x be the number of shares at $13 and\r\n" );
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document.write( "let y be the number of shares at $26.\r\n" );
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document.write( "Then you have these two equations\r\n" );
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document.write( "  x +   y =  150,             (1)     (counting shares)\r\n" );
document.write( "13x + 26y = 2860  dollars     (2)     (counting dollars)\r\n" );
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document.write( "These are your basic equations, and as soon as you got this system, the setup is completed.\r\n" );
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document.write( "There are different methods of solving such system (Substitution, Elimination, using determinants). \r\n" );
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document.write( "I will use the Elimination method here. \r\n" );
document.write( "Divide equation (2) by 13 (both sides, You will get this equation in this equivalent form\r\n" );
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document.write( "x + 2y = 220.             (3)\r\n" );
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document.write( "Now subtract eq(3) from eq(1).  x-terms will cancel each other, and  you will get an expression for unknown y\r\n" );
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document.write( "y =  220-150 = 70.      \r\n" );
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document.write( "Thus, you found number of shares at $26. It is 70. \r\n" );
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document.write( "Hence the number of shares at $13 was 150 - 70 = 80.\r\n" );
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document.write( "Check.  80*13 + 26*70 = 2860 dollars.   ! Correct. !\r\n" );
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document.write( "Answer.  80 shares at $13 and 70 shares at $26.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2   (one equation approach)\r
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document.write( "Let x be the number of shares at $13.\r\n" );
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document.write( "Then the number of shares at $6 is (15-x),  according to the condition.\r\n" );
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document.write( "It was payed  13*x        dollars for x        13-dollar shares.\r\n" );
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document.write( "It was payed  26*(150-x)  dollars for (150-x)  26-dollar shares.\r\n" );
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document.write( "Summing up these money, you get the \"money\" equation\r\n" );
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document.write( "13x + 26*(150-x) = 2860.     (4)\r\n" );
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document.write( "It is your basic equation in the frame of this approach,\r\n" );
document.write( "and as soon as you got this equation, the setup is completed.\r\n" );
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document.write( "To solve equation (4), simplify it step by step.\r\n" );
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document.write( "13x + 3900 - 26x = 2860  ====>  -13x = 2860 - 3900 = -1040  ====>  x = \"%28-1040%29%2F%28-13%29\" = 80.\r\n" );
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document.write( "Thus you get 80 shares at $13 dollars.\r\n" );
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document.write( "Surely, you got the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 3   (Logical analysis)\r
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document.write( "Let assume for a minute that all shares are at $13.\r\n" );
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document.write( "Then their total cost would be 150*13 = 1950 dollars.\r\n" );
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document.write( "But it is by 2860 - 1950 = 910 dollars less than the given total cost.\r\n" );
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document.write( "Why did we get the difference ?  - But of course, because we account 26-dollar shares as 13-dollar shares.\r\n" );
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document.write( "So, we should return these 26-dollar shares back. Returning each, we diminish the difference of $910 by  26-13 = 13 dollars.\r\n" );
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document.write( "Then it is clear that the number of 26-dollar shares was  \"910%2F13\" = 70,  exactly as in the solutions 1 and 2 above.\r\n" );
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document.write( "Hence, the number of $13 shares was  150 - 70 = 80, \r\n" );
document.write( "and you got the same answer.\r\n" );
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\n" ); document.write( "Congratulations !   You are now familiar with 3 methods for shares problems solution.\r
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\n" ); document.write( "\n" ); document.write( "I suggest that algebraic methods will be your basic methods for such problems,\r
\n" ); document.write( "\n" ); document.write( "and the logical analysis method will allow you to solve the problems MENTALLY without using equations.\r
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\n" ); document.write( "So, this share problem solution is the same as the traditional ticket problem solution.\r
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\n" ); document.write( "\n" ); document.write( "To see similar solved problems on tickets, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on tickets \r
\n" ); document.write( "\n" ); document.write( "    - Three methods for solving standard (typical) problems on tickets\r
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\n" ); document.write( "\n" ); document.write( "To see how the logical method works for other similar problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on two-wheel and three-wheel bicycles\r
\n" ); document.write( "\n" ); document.write( "    - Problem on animals at a farm\r
\n" ); document.write( "\n" ); document.write( "    - Problem on pills in containers\r
\n" ); document.write( "\n" ); document.write( "    - What type of problems are these? \r
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