Question 249946: write a system of equations that could be used to solve the following problem. solve using elmination.
jana opened her coin purse and found dimes, quarters and nickels with a total value of $1.90. there are twice as many dimes as quarters and half as many nickels as quarters. how many coins of each type did Jana have in her purse?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! 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.
.
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
.
5(1/2q) + 10(2q) + 25q = 190
.
Multiply by 2 to eliminate the fraction
5q + 40q + 50q = 380
.
95q = 380
.
q = 4
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She has 4 quarters = 100 cents = $1.00
.
d = 2q = 2(4) = 8
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She has 8 dimes = 80 cents = $.80
.
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.
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