Question 1206418
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A shop owner paid a total of $2385 for some shirts and ties. 
Each shirt cost $14 less than each tie. 
The number of ties bought was 2/3 of the number of shirts bought. 
He paid $127.80 more for the ties than the shirts.
(a) How much did he pay for all the shirts?
(b) How many ties did he buy?
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<pre>
(a)  Let x be the amount he paid for all the shirts.

     Then the amount which he paid for all the ties was by (x+127.80)  dollars.

     An equation for the total is 

                 x + (x+127.80) = 2385  dollars.


     Simplify and find x

           2x = 2385 - 127.80

           2x = 2257.20

            x = 2257.20/2 = 1128.60.


     Thus part (a) is solved.



(b)  Let x be the number of shirts.

     Then the number of ties is  {{{(2/3)x}}}.


     We just found in (a) the cost of all shirts. It is 1128.60 dollars.

     Hence, the cost of all ties is  2385 - 1128.60 = 1256.40 dollars.


     The price of one shirt is then  {{{1128.60/x}}}.

     The price for one tie  is  {{{1256.40/((2/3)x)}}} = {{{1884.60/x}}}.


     The difference of prices is 14 dollars (given).


     So, we write this "price equation"

         {{{1884.60/x}}} - {{{1128.60/x}}} = 14.


     Simplify and find x

         {{{(1884.60-1128.60)/x}}} = 14

         {{{756/x}}} = 14

         x = {{{756/14}}} = 54.


     Thus the number of shirts was 54.

     Then the number of ties was  {{{(2/3)*54}}} = 36.


     At this point, part (b) is solved, too, and the <U>ANSWER</U> is 36 ties.
</pre>

The problem is solved in full &nbsp;( = completely).