SOLUTION: PLEASE HELP SOLVE: BANK WITH 47 COINS. SOME ARE QUARTERS AND THE REST ARE HALF DOLLARS. IF THE TOTAL VALUE OF THE COINS IS $17.00, HOW MANY OF EACH DENOMINATION DOES SHE HAVE?

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Question 53649: PLEASE HELP SOLVE:
BANK WITH 47 COINS. SOME ARE QUARTERS AND THE REST ARE HALF DOLLARS. IF THE TOTAL VALUE OF THE COINS IS $17.00, HOW MANY OF EACH DENOMINATION DOES SHE HAVE?
Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website!
Let the number of quarters=x
Let the number of half dollars equal the rest of the 47 coins=47-x
The amount of money you have is the (worth of the coin)*(number of coins)
So you have:
Money in Quarters=.25x
Money in half dollars=.50(47-x)
Total amount of money=17.00
So your problem to solve is:
.25x+.50(47-x)=17.00
If you're like me, decimals are just mistakes waiting to happen. We can eliminate our decimals by multiplying both sides of the equation by 100.
100(.25x)+100(.50)(47-x)=100(17.00)
25x+50(47-x)=1700
25x+50(47)+50(-x)=1700
25x+2350-50x=1700
(25-50)x+2350=1700
-25x+2350=1700
-25x+2350-2350=1700-2350
-25x=-650
-25x/-25=-650/-25
x=26
The amount of quarters you have is:x=26
The amount of half dollars that you have:47-x=47-26=21
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Check, does 26 quarters + 21 half dollars = $17.00?
26(.25)+21(.50)
=$6.50+$10.50
=$17.00
Seems like a valid conclusion to me. How about you?