SOLUTION: Sarah has a collection of nickels, dimes, and quarters worth $15.75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she
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-> SOLUTION: Sarah has a collection of nickels, dimes, and quarters worth $15.75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she
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Question 68149This question is from textbook Algebra for College Students
: Sarah has a collection of nickels, dimes, and quarters worth $15.75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have? This question is from textbook Algebra for College Students
You can put this solution on YOUR website! Write an equation for each statement:
:
"Sarah has a collection of nickels, dimes, and quarters worth $15.75."
.05n + .1d + .25q = 15.75
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"She has 10 more dimes than nickels"
d = n + 10
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"twice as many quarters as dimes."
q = 2d
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How many coins of each kind does she have?
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Take the 2nd equation and arrange it so n is in terms of d also
n + 10 = d
n = (d - 10)
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In the 1st equation substitute (d-10) for n and 2d for q:
.05n + .1d + .25q = 15.75
:
.05(d-10) + .1d + .25(2d) = 15.75
:
.05d - .5 + .1d + .5d = 15.75
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.65d - .5 = 15.75
:
.65d = 15.75 + .5
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.65d = 16.25
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d = 16.25/.65
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d = 25 dimes
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Remember the statement "twice as many quarters as dimes."
q = 2(25)
q = 50 quarters
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The statement "She has 10 more dimes than nickels"
n = 25 - 10
n - 15 nickels
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Check our solutions
.05(15) + .1(25) + .25(50) =
.75 + 2.50 + 12.50 = 15.75 proves our solutions
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How about this? Did it make sense to you??
