<PRE><B>Question 1141370</B>
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The information is given in such a way that the numbers of 5-cent and 10-cent coins are both defined in terms of the number of 1-cent coins.  So choosing x to represent the number of 1-cent coins should make the problem easiest.&lt;br&gt;
Let x = # of 1-cent coins
Then 3x = # of 5-cent coins
And x-2 = # of 10-cent coins&lt;br&gt;
Now write and solve the equation that says the total value is $1.10, or 110 cents:&lt;br&gt;
{{{10(x-2)+5(3x)+1(x) = 110}}}&lt;br&gt;
You can finish solving the problem from there....&lt;br&gt;
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You can also solve the problem informally using logical reasoning.&lt;br&gt;
(1) The total value of all the coins (110) is a multiple of 5; and the total value of all the 5- and 10-cent coins is a multiple of 5.  That means the total value of the 1-cent coins must be a multiple of 5 -- i.e., the number of 1-cent coins is a multiple of 5.&lt;br&gt;
(2) So the number of 1-cent coins is 5, or 10, or 15, ....&lt;br&gt;
(3) But the number of 5-cent coins is 3 times the number of 1-cent coins.  If the number of 1-cent coins were 10, the number of 5-cent coins would be 30; and 30 5-cent coins is more than the actual total value of all the coins.&lt;br&gt;
(4) So the number of 1-cent coins HAS TO BE 5.  Then the number of 5-cent coins is 3*5 = 15, and the number of 10-cent coins is 5-2 = 3.&lt;br&gt;
CHECK: 3(10)+15(5)+5(1) = 30+75+5 = 110&lt;br&gt;
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Knowing how to solve problems like this using formal algebra is of course useful... but it is excellent brain exercise to be able to solve them using logical reasoning.</PRE>