Question 1165655
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If a formal algebraic solution is not required, you can get some good mental exercise by solving this using logical reasoning and some mental arithmetic.<br>
(1) Take the 4 "extra" dimes and set them aside; then arrange the remaining coins into groups of 2 dimes and 1 nickel.<br>
(2) The value of the 4 dimes is $0.40; the value of all the coins is $13.40.  So the value of the groups of dimes and nickels is $13.00.<br>
(3) The value of 2 dimes and 1 nickel is $0.25, or 25 cents.  The number of those groups required to make $13.00, or 1300 cents, is 1300/25 = 52.<br>
(4) So there are 52 groups each containing 2 dimes and 1 nickel, plus the other 4 dimes.  That makes the number of dimes 2(52)+4 = 104+4 = 108 and the number of nickels 52.<br>
ANSWER: 108 dimes, 52 nickels.<br>
CHECK: 108(10)+52(5) = 1080+260 = 1340<br>