Question 1199194
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Given facts:<ol><li>James spent $6780 on some watches and clocks. </li><li>The amount spent on watches was $2820 more than the amount spent on the clocks. </li><li>He bought 3/5 as many clocks as watches. </li><li>Each clock cost $25 less than each watch. </li></ol>Let
w = number of watches


Since 3/5 = 0.6, we can use fact 3 to say:
0.6w = number of clocks


Now let
x = cost of 1 watch
which would mean
x-25 = cost of 1 clock
due to fact 4



1 watch = x dollars
w number of watches = wx dollars
1 clock = (x-25) dollars
0.6w number of clocks = 0.6w(x-25) dollars


Add these subtotals to get $6780 spent on everything
Refer to fact 1 above.
watches + clocks = 6780 total
wx + 0.6w(x-25) = 6780
wx + 0.6wx - 0.6w*25 = 6780
1.6wx - 15w = 6780
Pause here for now. We'll come back to this later.


Fact 2 can be rephrased as:
"The amount spent on clocks was $2820 less than the amount spent on the watches"
which means:
wx = amount spent on watches
wx-2820 = amount spent on clocks


Those two subtotals also add to 6780, due to fact 1.
wx+(wx-2820) = 6780
2wx-2820 = 6780
2wx = 6780+2820
2wx = 9600
wx = 9600/2
wx = 4800
Buying w number of watches, at x dollars a piece, cost $4800.


wx-2820 = 4800-2820 = 1980
and the clocks cost $1980.


We'll now return to the previous equation we paused at.
Plug in wx = 4800
So,
1.6wx - 15w = 6780
1.6(wx) - 15w = 6780
1.6*(4800) - 15w = 6780
7680 - 15w = 6780
-15w = 6780-7680
-15w = -900
w = -900/(-15)
w = 60
James bought 60 watches.
Each watch costs x = (wx)/w = 4800/60 = 80 dollars.



0.6w = number of clocks
0.6w = 0.6*60
0.6w = 36
and he also bought 36 clocks.
Each clock costs x-25 = 80-25 = 55 dollars.
He spent 36*55 = 1980 dollars on clocks as mentioned earlier.


The two subtotals should add to 6780 dollars.
watches + clocks = 4800+1980 = 6780
This helps confirm the answers.


Further confirmation is to note that
4800-1980 = 2820
which matches up with fact 2


There's probably a much more faster/efficient way to solve this.
Feel free to explore other options.


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Answer: 
60 watches + 36 clocks
96 total items.
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