Question 231070
In a piggy bank, there are twice as many dimes as quarters,
d = 2q
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five times as many nickels as quarters,
n = 5q
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and twice as many pennies as all other coins combined.
p = 2(n + d + q)
(1/2)p - n - d - q = 0
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Rearrange:
0p + 0n + d -2q = 0
0p +  n +0d -5q = 0
(1/2)p-n- d - q = 0 
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Change to an augmented matrix:
0p + 0n + d = 2q 
0p +  n +0d = 5q
p  - 2n -2d = 2q
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Solve p,d,and n for q:
d = 2q from the 1st equation:
n = 5q
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p = 2(5q)+2(2q)+ 2q
p =  16q
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There are a total of 24q coins
P(q) = 1/24 ; P(p)=16/24; P(n)=5/24 ; P(d)= 2/24
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Calculate the probability that either a nickel or a quarter will fall out. Express your solution as a fraction in lowest terms.
P(nickel or quarter) = P(nickel) + P(quarter) = (5/24)+(1/24) = 1/4
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Cheers,
Stan H.