Question 249946
With coin problems you have to keep track of the number of coins and the value of the coins. Usually these create two linear equations.
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Jana found she had nickels, dimes, and quarters with a total value of $1.90 = 190 cents.
The total value obviously is a value problem, so:
5n + 10d + 25q = 190
, where
n = number of nickels
d = number of dimes
q = number of quarters
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But we need to figure out the number of coins, n, d, and q.
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We are told in the problem:
d = 2q        twice as many dimes as quarters
n = 1/2q    half as many nickels as quarters
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Substituting into the value equation, we have
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5(1/2q) + 10(2q) + 25q = 190
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Multiply by 2 to eliminate the fraction
5q + 40q + 50q = 380
.
95q = 380
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q = 4
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She has 4 quarters = 100 cents = $1.00 
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d = 2q = 2(4) = 8
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She has 8 dimes = 80 cents = $.80
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n = 1/2q  = 1/2(4) = 2
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She has 2 nickels = 10 cents = $.10
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Adding up the dollar amounts, she has $1.90.
.
That checks.
Done.