Question 122631This question is from textbook Introductory Algebra
: A storekeeper goes to the bank to get $10 worth of change. She requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickels as dimes, and no pennies or dollars. How many of each coin did the storekeeper get?
This question is from textbook Introductory Algebra
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! I'll tell you what happens in the real bank ... she gets no change at all because no teller is
going to be able to figure that out rapidly if at all ... and the customers waiting in line
behind her will get mad too. It wouldn't be pretty, that's for sure.
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But that doesn't teach us anything about algebra. So let's work the problem ...
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Let H = the number of half dollars, Q = the number of quarters, D = the number of dimes, and
N = the number of nickels.
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The problem tells you that the number of quarters is two times the number of half dollars. So
we can write the equation:
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Q = 2*H
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The next thing the problem says is that the number of dimes is two times the number of
quarters. But the number of quarters (from above) is 2*H. Therefore, the number of dimes
being two times that results in:
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D = 2*(2*H) = 4*H
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Finally, the problem says that the number of nickels is 3 times the number of dimes (which
is 4*H). So the number of nickels is:
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N = 3*(4*H) = 12*H
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Each half dollar is $0.50. Each quarter is $0.25. Each dime is $0.10. And each nickel is $0.05.
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So if we multiply the worth of each coin times the number of coins, the total amount is to be
$10. So we can write the equation:
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0.50*H + 0.25*Q + 0.10*D + 0.05*N = 10
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Now we can substitute the values that we got above for Q, D, and N to get:
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0.50*H + 0.25(2*H) + 0.10(4*H) + 0.05(12*H) = 10
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Doing the multiplication results in:
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0.50*H + 0.50*H + 0.4*H + 0.6*H = 10
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Adding all the terms on the left side results in:
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2*H = 10
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and we can solve for H (which is the number of halves) by dividing both sides by 2 to get:
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H = 10/2 = 5
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There are 5 half dollars. And since the number of quarters is double that, there are 10 quarters,
and since the number of dimes is twice the number of quarters, there are 20 dimes. And
finally, since the number of nickels is 3 times the number of dimes, there are 60 nickels.
.
Let's check the answers ... 5 half dollars is $2.50. 10 quarters is also $2.50. 20 dimes is
$2.00. And 60 nickels is $3.00. The total is $2.50 + $2.50 + $2.00 + $3.00 and that adds
up to the $10 it is supposed to be.
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Hope this helps you to understand the problem.
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