document.write( "Question 1210324: The product of the ages of Adu and Tanko is 9 less than Akorfa's age. If Tanko is 4 years older than Adu and Akorfa's age is six times Tanko's age, find Akorfa's age. \n" ); document.write( "

Algebra.Com's Answer #851892 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The product of the ages of Adu and Tanko is 9 less than Akorfa's age.
\n" ); document.write( "If Tanko is 4 years older than Adu and Akorfa's age is six times Tanko's age, find Akorfa's age.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let x be the Tanko's age (in years).\r\n" );
document.write( "\r\n" );
document.write( "Then the Adu's age is (x-4) years and the Akorfa's age is 6x years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the problem, we are given that \r\n" );
document.write( "\r\n" );
document.write( "    x*(x-4) = 6x-9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and find x\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - 4x = 6x - 9\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - 4x - 6x + 9 = 0\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - 10x + 9 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor left side\r\n" );
document.write( "\r\n" );
document.write( "    (x-1)*(x-9) = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, there are two potential solutions for x:  x= 1  and  x= 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "But value x= 1 does not work, since then x-4 is negative (the Adu's age).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus, the only possible age for Tanko is 9 years.\r\n" );
document.write( "\r\n" );
document.write( "Then Adu is 9-4 = 5 years old;  Akotfa is 6*9 = 54 years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  Adu is 5, Tanko is 9, Akorfa is 54.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Obviously, this problem is to teach a student to construct a single quadratic equation
\n" ); document.write( "for the problem and then to solve it on his/her own using a standard methodology.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "///////////////////////////////\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Added after reading the post by @greenestamps.

\r
\n" ); document.write( "\n" ); document.write( "        I said \" obvious \" in my post, because it is really obvious, at least for me.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        I do not see any arrogance in it.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        And I really think that the solution in my post is a right way to teach.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I don't see any arrogance in my post, but I do see a desire from one of the tutors
\n" ); document.write( "to kick me for no reason and belittle the importance of my posts and my work on this forum.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Dear tutors, every time as you will do it, I will answer adequately.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/////////////////////////////////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Edwin asks in his post \"Where's it all going? Damned if I know.\",
\n" ); document.write( "connecting it to teaching Math, calculators, computers and AI.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Edwin, teaching Math means\r\n" );
document.write( "\r\n" );
document.write( "    (1) teaching students to think - - - it is the major goal.\r\n" );
document.write( "\r\n" );
document.write( "    (2) teaching students to solve certain class of problems by certain methods.\r\n" );
document.write( "\r\n" );
document.write( "    (3) developing students' common sense, feeling of responsibility, honesty.\r\n" );
document.write( "\r\n" );
document.write( "    (4) teaching them and explaining them what is good and what is bad, \r\n" );
document.write( "        and also why Math is perfect, harmonic, beautiful and effective.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "These goals are the same as they were hundreds and thousands years ago (recall Euclid !) - they are with no change.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "100 and 200 years ago people used accounting abacus - it helped them to count.\r\n" );
document.write( "But it did not replace thinking.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "100 and 80 years ago people used trigonometric and logarithm tables.\r\n" );
document.write( "They helped people to calculate.  But they did not replace thinking.\r\n" );
document.write( "And where are those Tables now ?\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "40 and 20 years ago calculators helped.\r\n" );
document.write( "But calculators did not replace thinking.  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then computers came, and I solved partial differential equations numerically \r\n" );
document.write( "to simulate structures behavior and processes in Civil engineering.\r\n" );
document.write( "Did computers replace thinking ? - No.  They made the possibilities wider, but did not replace thinking.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Online tools, online calculators came to help - but they did not replace thinking.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Artificial intelligence (in form of deep learning) may help teachers - by feeding them with knowledge.  \r\n" );
document.write( "But AI can not and should not replace thinking. If it replace - a catastrophe will come. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the same way, AI will not replace Math in Math, in Science and in teaching.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We should distinct Math, Computer Science, and AI.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "They are different essences/subjects/disciplines and do not replace each other.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Those who want study Math - let them learn Math.\r\n" );
document.write( "Those who want study Computer Science - let them learn Computer Science, big data and algorithms.\r\n" );
document.write( "Those who want develop AI, learn AI and apply AI - let them do it.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simply do not mix different essences.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Ancient Greeks said: identify the same and distinguish the different.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For them, this principle was the base of philosophy.\r\n" );
document.write( "\r\n" );
document.write( "They thought that this principle is the base to everything.\r\n" );
document.write( "

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

\n" );