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Molly has $14.10 in coins. She has five more nickels than dimes. She has seven fewer quarters than dimes. How many quarters does she have?

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2 Answers

$14.10
 
Let N be the number of nickels.
Let Q be the number of quarters.
Let D be the number of dimes.
 
N = 5 + D
Q = D - 7
 
.25(D - 7) + .05(5 + D) + .10(D) = 14.10
 
.25D - 1.75 + .25 + .05D + .10D = 14.10
 
.4D - 1.5 = 14.10
 
.4D = 14.10 + 1.50
 
.4D = 15.60
 
D = 39
 
Q = 39 - 7
 
Q = 32
 
 
Hey Sabrina -- you may like this "kitchen-table" approach ... start with $10 of 40Q ...
that means 47 dimes and 52 nickels, putting us at 10 + 4.70 + 2.60 => overshooting 3.20 ...
for every Q removed, lose a dime & nickel or 40 cents ==> drop 8Q to 32Q, 39D, 44N ...
8 + 3.90 + 2.20 = $14.10 check ... Call this a "stair-step" approach: start simple & step to the answer :)