SOLUTION: A piggy bank contains $18.30 made up of loonies, quarters, and nickels. There are 3 more quarters than loonies and twice as many nickels than loonies. How many of each coin are the

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Question 959277: A piggy bank contains $18.30 made up of loonies, quarters, and nickels. There are 3 more quarters than loonies and twice as many nickels than loonies. How many of each coin are there?
Found 3 solutions by macston, josgarithmetic, MathTherapy:
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
L=loonies; Q=quarters=L+3; N=nickels=2L
$1L+$0.25Q+$0.05N=$18.30 Substitute for Q and N
$1L+$0.25(L+3)+$0.05(2L)=$18.30
$1L+$0.25L+$0.75+$0.10L=$18.30 Subtract $0.75 from each side.
$1.35L=$17.55 Divide each side by $1.35
L=13 ANSWER 1: There were 13 loonies.
Q=L+3=13+3=16 ANSWER 2: There were 16 quarters.
N=2L=2(13)=26 ANSWER 3: There were 26 nickels.
CHECK:
$1L+$0.25Q+$0.05N=$18.30
$1.00(13)+$0.25(16)+$0.05(26)=$18.30
$13.00+$4.00+$1.30=$18.30
$18.30=$18.30



Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
The value of one loony is unknown. Let L = fraction of dollar for 1 loony, which may be mixed or whole value.
Let x be how many loonies.

Three equations in four unknown variables, L, x, q, n.







, not a linear equation. Solutions must use x as a whole number. L must be a positive real number RATIONAL




, now this equation form allows picking any of several whole number values for x, and finding any fitting values for L.

, and notice that there is a restriction here for x and for L, again, L must be positive. Necessary, .
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A piggy bank contains $18.30 made up of loonies, quarters, and nickels. There are 3 more quarters than loonies and twice as many nickels than loonies. How many of each coin are there?
Let the number of loonies (Canadian dollar coins), be L

Then number of quarters = L + 3

Number of nickels: 2L

We the get: L + .25(L + 3) + .05(2L) = 18.3

L + .25L + .75 + .1L = 18.3

L + .25L + .1L = 18.3 - .75

1.35L = 17.55

L, or number of loonies = , or 

Number of quarters: 13 + 3, or 

Number of nickels: 2(13), or  

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