Question 23737: In Paul's bank, there is $2.60 in pennies, nickels, and dimes. In all there are 45 coins. If there are twice as many nickels as pennies, find out how many of each kind there are.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Let x = number of pennies, (since this is at the end of the first phrase).
2x = number of nickels
Now, getting the number of dimes is a little tricky. You have accounted for a total of x + 2x = 3x in pennies and nickels, and there are a total of 45 coins in all. The number of dimes is 45 minus all the rest of the coins. That is,
45 - 3x = number of dimes
Values of the coins in CENTS will be the value of each coin times the number of coins:
1*x = value of pennies
5*(2x) = value of nickels
10*(45-3x) = value of dimes
The equation is based upon the total value of the coins. Be sure that if you are doing the problem in cents, then everything is in cents:
1x + 5(2x) + 10(45-3x) = 260 cents
1x + 10x + 450 - 30x = 260
-19x + 450 = 260
Subtract 450 from each side:
-19x + 450 -450 = 260-450
-19x = -190
Divide both sides by -19 and HOPE it comes out even!! Remember, it CAN'T come out to a fraction, and it CAN'T come out to a negative number!
x = 10 Pennies
2x = 20 Nickels
45-3x = 45 - 30 = 15 Dimes
Check the values:
P = $0.10
N = $1.00
D = $1.50
Total= $2.60
It checks!
R^2 at SCC
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