Question 1162246
<br>
A student just learning algebra should certainly know how to solve the problem using formal algebra, as shown by the other tutor.<br>
But solving a problem like this informally, with logical reasoning and simple arithmetic, is good mental exercise.  It might go something like this:<br>
(1) If all 19 coins were nickels, the total face value would be 95 cents; the actual value is $1.55, or 155 cents.  The difference is 60 cents.
(2) Exchanging a nickel for a dime keeps the number of coins the same and increases the face value by 5 cents.
(3) The number of times a nickel needs to be exchanged for a dime, to make up the difference of 60 cents, is 60/5 = 12.
(4) Therefore, the collection contains 12 dimes and 19-12 = 7 nickels.<br>