Question 1210324
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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.
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<pre>
Let x be the Tanko's age (in years).

Then the Adu's age is (x-4) years and the Akorfa's age is 6x years.


From the problem, we are given that 

    x*(x-4) = 6x-9.


Simplify and find x

    x^2 - 4x = 6x - 9

    x^2 - 4x - 6x + 9 = 0

    x^2 - 10x + 9 = 0


Factor left side

    (x-1)*(x-9) = 0


So, there are two potential solutions for x:  x= 1  and  x= 9.


But value x= 1 does not work, since then x-4 is negative (the Adu's age).


Thus, the only possible age for Tanko is 9 years.

Then Adu is 9-4 = 5 years old;  Akotfa is 6*9 = 54 years.


<U>ANSWER</U>.  Adu is 5, Tanko is 9, Akorfa is 54.
</pre>

Solved.


Obviously, this problem is to teach a student to construct a single quadratic equation 
for the problem and then to solve it on his/her own using a standard methodology.



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<H3>Added after reading the post by @greenestamps.</H3>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I said &nbsp;" obvious " &nbsp;in my post, &nbsp;because it is really obvious, &nbsp;at least for me.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I do not see any arrogance in it.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;And I really think that the solution in my post is a right way to teach.



I don't see any arrogance in my post, &nbsp;but I do see a desire from one of the tutors 
to kick me for no reason and belittle the importance of my posts and my work on this forum.



Dear tutors, every time as you will do it, I will answer adequately.



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Edwin asks in his post "Where's it all going? Damned if I know.",
connecting it to teaching Math, calculators, computers and AI.


<pre>
Edwin, teaching Math means

    (1) teaching students to think - - - it is the major goal.

    (2) teaching students to solve certain class of problems by certain methods.

    (3) developing students' common sense, feeling of responsibility, honesty.

    (4) teaching them and explaining them what is good and what is bad, 
        and also why Math is perfect, harmonic, beautiful and effective.


These goals are the same as they were hundreds and thousands years ago (recall Euclid !) - they are with no change.


100 and 200 years ago people used accounting abacus - it helped them to count.
But it did not replace thinking.


100 and 80 years ago people used trigonometric and logarithm tables.
They helped people to calculate.  But they did not replace thinking.
And where are those Tables now ?


40 and 20 years ago calculators helped.
But calculators did not replace thinking.  


Then computers came, and I solved partial differential equations numerically 
to simulate structures behavior and processes in Civil engineering.
Did computers replace thinking ? - No.  They made the possibilities wider, but did not replace thinking.


Online tools, online calculators came to help - but they did not replace thinking.


Artificial intelligence (in form of deep learning) may help teachers - by feeding them with knowledge.  
But AI can not and should not replace thinking. If it replace - a catastrophe will come. 


In the same way, AI will not replace Math in Math, in Science and in teaching.


We should distinct Math, Computer Science, and AI.


They are different essences/subjects/disciplines and do not replace each other.


Those who want study Math - let them learn Math.
Those who want study Computer Science - let them learn Computer Science, big data and algorithms.
Those who want develop AI, learn AI and apply AI - let them do it.


Simply do not mix different essences.


Ancient Greeks said: identify the same and distinguish the different.


For them, this principle was the base of philosophy.

They thought that this principle is the base to everything.
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