Question 1205537: Lucas has 37 coins, all nickels and dimes in his piggy bank. The value of the coins is $3.10. How many dimes does Lucas have? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52787) (Show Source):
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Lucas has 37 coins, all nickels and dimes in his piggy bank.
The value of the coins is $3.10. How many dimes does Lucas have?
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D dimes; (37-D) nickels.
Write the total money equation
10*D + 5*(37-D) = 310 cents.
Solve it and find D
10*D + 5*37 - 5*D = 310
10*D - 5*D = 310 - 5*37
5*D = 125
D = 125/5 = 25.
ANSWER. 25 dimes.
The typical formal algebraic solution shown by the other tutor is of course fine; you should understand it and be able to solve similar problems by that method.
For a mental solution method....
Note that if all 37 coins were dimes the total value would be $3.70.
That is $0.60 more than the actual total of $3.10.
Since each nickel is worth $0.10-$0.05 = $0.05 less than each dime, the number of nickels must be $0.60/$0.05 = 60/5 = 12.
Therefore the number of dimes is 37-12 = 25
ANSWER: 25
Note this method can be used to solve a wide range of similar problems quickly, without formal algebra.
