Question 1199194
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James spent $6780 on some watches and clocks. 
The amount spent on watches was $2820 more than the amount spent on the clocks. 
He bought 3/5 as many clocks as watches. 
Each clock cost $25 less than each watch. 
What was the total number of watches and clocks bought by James?
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        The solution consists of two parts (two steps) and uses 
        two clear simple ideas, accompanying with short calculations.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>First step</U>



<pre>
Let X be the amount of money spent on watches, Y be the amount of money spent on clocks.


From the condition, we have two equations

    X + Y = 6780     (total dollars)
    X - Y = 2820     (X is $2820 more than Y)


To find X, add the equations. You will get  2X = 6780+2820 = 9600,  X = 9600/2 = 4800 dollars.

To find Y, subtract second equation from the first one. You will get  2Y = 6780-2820 = 3960,  Y = 3960/2 = 1980 dollars.
</pre>

First step is complete. &nbsp;We just found that the amount spent on watches was &nbsp;$4800;  &nbsp;the amount spent on clocks was  &nbsp;$1980.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Second step</U>



<pre>
Let W be the number of watches bought by James.

Then the number of clocks was  {{{(3/5)W}}} = 0.6W.


Each watch price was  {{{4800/W}}}  dollars;  each clock price was  {{{1980/(0.6*W)}}} = {{{3300/W}}}.

Next, the difference of prices is 25 dollars.  It gives this "price" equation

    {{{4800/W}}} - {{{3300/W}}} = 25.


Simplify and find W

    {{{1500/W}}} = 25

    W = {{{1500/25}}} = 60.


<U>ANSWER</U>.  60 watches and  {{{(3/5)*60}}} = 36 clocks.
         The total number of items was 60+36 = 96.
</pre>

Solved.



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The meaning of this problem is not to make tons of calculations.

The meaning is to find a right idea of solution.