Question 900905: Biff has a collection of pennies, nickels, dimes and quarters worth $2.73 altogether. He has twice as many nickels as dimes, one more nickel than quarters, and two more than twice as many pennies as nickels. How many of each kind of coin does Biff have?
Found 3 solutions by stanbon, richwmiller, MathTherapy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Biff has a collection of pennies, nickels, dimes and quarters worth $2.73 altogether. He has twice as many nickels as dimes, one more nickel than quarters, and two more than twice as many pennies as nickels. How many of each kind of coin does Biff have?
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Value Eq:: p + 5n + 10d + 25q = 273 cents
Quantity Eqs::
n = 2d ; so d = n/2
n = q+1 ; so q = n -1
n = 2p+2 ; so p = (n-2)/2
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Substitute for d,q, and p ; solve for n.
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(n-2)/2 + 5n + 10(n/2) + 25(n-1) = 273
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Solve for "n" and will be able to solve for p,n, and Q.
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Cheers,
Stan H.
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Answer by richwmiller(17219)  (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Biff has a collection of pennies, nickels, dimes and quarters worth $2.73 altogether. He has twice as many nickels as dimes, one more nickel than quarters, and two more than twice as many pennies as nickels. How many of each kind of coin does Biff have?
Let number of dimes be D
Then number of nickels = 2D
Number of quarters: 2D - 1
Number of pennies: 2(2D) + 2 , or 4D + 2
Therefore, .1D + .05(2D) + .25(2D - 1) + .01(4D + 2) = 2.73
.1D + .1D + .5D - .25 + .04D + .02 = 2.73
.74D - .23 = 2.73
.74D = 2.96
D, or number of dimes =  , or 
Number of nickels: 2(4), or 
Number of quarters: 8 - 1, or 
Number of pennies: 4(4) + 2, or 
You can do the check!!
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