SOLUTION: Dave Bowers collects U.S. gold coins. He has a collection of 41 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $540, how many of each deno

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Question 320128: Dave Bowers collects U.S. gold coins. He has a collection of 41 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $540, how many of each denomination does he have?
Thank You.
Found 2 solutions by checkley77, Sunny Day:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
20X+10(41-X)=540
20X+410-10X=540
10X=540-410
10X=130
X=130/10
X=13 ANS. FOR THE NUMBER OF $20 COINS.
41-13=28 ANS. FOR THE NUMBER OF $10 COINS.
PROOF:
20*13+10*28=540
260+280=540
540=540

Answer by Sunny Day(15) About Me  (Show Source):
You can put this solution on YOUR website!
Let 'x' be the number of $10 coins.
he has a total of 41 coins and since the rest are $20 coins, the number $20 coins will be 41-x.
The face value of 'x' $10 coins = 10x
Face value of (41-x) $20 coins = 20(41-x)
So the face value of all the coins taken together will be
10x + 20(41-x) = 540
10x + 20X41 - 20x = 540
10x - 20x = 540 -820
-10x = -280
x = -280/-10
x = 28
so the number of $10 coins = 28
and the number of $20 coins = (41 - 28) = 13
[cross checking : 28 + 13 = 41
and 28X10 + 13X20 = 540]