SOLUTION: Jessica has twice as many dimes as nickels and five more quarters than nickels. If the value of all of her coins is $4.75, how many dimes does she have?

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Question 1133501: Jessica has twice as many dimes as nickels and five more quarters than nickels. If the value of all of her coins is $4.75, how many dimes does she have?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
COIN         COUNT      MONEY
Quarter      n+5        0.25(n+5)
Dime         2n          0.1(2n)
Nickel        n          0.05n
TOTAL                   4.75

0.25n%2B0.25%2A5%2B0.2n%2B0.05n=4.75
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0.5n%2B1.25=4.75
0.5n=3.50
n=3.5%2F0.5
n=7
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Number of dimes, 2n=2%2A7=highlight%2814%29

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor has shown you a perfectly good formal algebraic solution.

An informal solution using virtually the same calculations can be obtained using logical reasoning and some simple mental arithmetic.

(1) Set those "extra" 5 quarters aside. The remaining value is then $3.50; consisting of equal numbers of nickels and quarters, and twice that many dimes.
(2) Consider the value of one nickel, one quarter, and two dimes; it is $0.50.
(3) $3.50 is 7 times $0.50; so the $3.50 consists of 7 each of nickels and quarters, and twice that many dimes.

So there are 14 dimes.