document.write( "Question 1150213: Emily counts the triangles and parallelograms in an art piece and determines that there are altogether 42 triangles and parallelograms. If there are 150 total sides, how many triangles and parallelograms are there? \n" ); document.write( "

Algebra.Com's Answer #771596 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "Based on the context of the problem, I assume that these triangles and parallelograms are separate shapes / areas / figures\r\n" );
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document.write( "that are located at totally different parts of the art piece and do not intersect each other and do not have common\r\n" );
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document.write( "sides and/or vertices.\r\n" );
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document.write( "Then from the condition, you have this system of equations for the number of triangles T and the number of parallelograms  P\r\n" );
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document.write( "     T +  P =  42     (1)    (counting shapes altogether)\r\n" );
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document.write( "    3T + 4P = 150     (2)    (counting sides)\r\n" );
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document.write( "To solve the system, express  T = 42 - P  from equation (1) and substitute it into equation (2), replacing T there\r\n" );
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document.write( "    3*(42-P) + 4Q = 150.\r\n" );
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document.write( "Simplify step by step\r\n" );
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document.write( "    126 - 3P + 4P = 150\r\n" );
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document.write( "     P = 150 - 126 = 24.\r\n" );
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document.write( "ANSWER.  There are 24 parallelograms and 42-24 = 18 triangles in the art piece.\r\n" );
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document.write( "CHECK.   4*24 + 18*3 = 150,  the total number of sides.   ! Precisely correct !\r\n" );
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