Question 1145593
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            From the first glance,  this problem is for  3  equations in three unknowns.


            But actually,  it can be easily solved using only  ONE  single equation in  ONE  unknown.


            I will show you how to do it.



<U>Solution</U>


<pre>
Let  x be the number of polo shirts.

Then the number of rugby shirts is 2x, according to the condition.

And the number of T-shirts is then (200-x-2x) = 200-3x.


The total cost equation is then


    24*x + 36*(2x) + 12*(200-3x) = 6000.


Simplify and solve for x :


    24x + 72x + 12*200 - 36x = 6000,

    60x                      = 6000 - 12*200

      x                      = {{{(6000-12*200)/60}}} = 60.


<U>ANSWER</U>.  60 polo shirts;  60*2 = 120 rugby shirts and the rest, (200-60-2*60) = 20 are T-shirts.
</pre>

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The benefit of this approach is that students may start solving such problems much earlier than they start learning systems of equations.


I think that the true goal of this problem is to teach students to this approach.


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To see other similar solved problems, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/More-complicated-word-problems-to-solve-using-single-linear-equation.lesson>More complicated word problems to solve using a single linear equation</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/Advanced-word-problems-to-solve-by-reduction-to-single-linear-equation.lesson>Advanced word problems to solve using a single linear equation</A>

in this site.