Question 1199194: 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?
Found 3 solutions by math_tutor2020, MathTherapy, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Given facts:- 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.
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.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
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?
Let amount spent on watches be W
Since a total of $6,780 was spent on watches and clocks, amount spent on clocks = 6,780 - W
Since amount spent on watches was $2,820 more than what was spent on clocks, then amount spent on clocks = W - 2,820
We then get: 6,780 - W = W - 2,820
- W - W = - 2,820 - 6,780
- 2W = - 9,600
Amount spent on watches =, or 
Since $4,800 was spent on watches, amount spent on clocks = 6,780 - 4,800 = $1,980
Now, let number of watches purchased be W, and cost of each watch, C
Then number of clocks purchased =  , and cost of each clock: C - 25
With total spent on watches being 4,800, we get: WC = 4,800 ----- eq (i)
Also, with total spent on clocks being $1,980, we get: 
3WC - 75W = 9,900 ----- Multiplying by LCD, 5 ----- eq (ii)
3(4,800) - 75W = 9,900 ----- Substituting 4,800 for WC in eq (ii)
14,400 - 75W = 9,900
- 75W = 9,900 - 14,400
- 75W = - 4,500
Numner of watches purchased, or 
Number of clocks purchased:
Answer by ikleyn(52786)  (Show Source):
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