document.write( "Question 1173010: Bianca and her father picked 109 apples. Bianca's father picked 13 more apples than triple the apples Bianca picked. How many apples did each pick? \n" ); document.write( "

Algebra.Com's Answer #798164 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "    Bianca  +  Father    = 109    (in total)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "      B     +  (3B + 13) = 109\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "      B     + 3B   + 13  = 109\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         4B              = 109 - 13\r\n" );
document.write( "\r\n" );
document.write( "         4B              = 96\r\n" );
document.write( "\r\n" );
document.write( "          B              = 96/4 = 24.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  Bianca picked 24 apples.  The father picked 3*24 + 13 = 85 apples.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  24 + 85 = 109, in total.   ! Precisely correct !\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Which approach to use - one equation or two equations ? ? ?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It mostly depends on the age, level/grade and readiness of the student . . . \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Young students may not know systems of two equations - - - then only one equation approach does work.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As the student becomes older, he (or she) is able to adopt the two equations approach.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I always try to guess from the context, which age and which level the student is - and react accordingly.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A mature student, ideally, should know both approaches; freely manipulate with either approach
\n" ); document.write( "and understand when and why they both are equivalent.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Then the issue on which approach to use is only the question of taste and traditions . . . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "With two small additions.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "1.  One equation approach gives the opportunity for earlier education and \r\n" );
document.write( "\r\n" );
document.write( "    earlier involvement of a young student to problems solving - - - comparing with the two-equation approach.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  There is a class of problems, which are, from the first glance, for 3-equation approach,\r\n" );
document.write( "\r\n" );
document.write( "    but actually can be easily solved using 1-equation approach.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    For this class of problems, it is CONCEPTUALLY IMPORTANT to teach young students to make right setup.\r\n" );
document.write( "\r\n" );
document.write( "    It is the moment, when right teaching really helps to built young minds in a right way.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );