<PRE><B>Question 1122469</B>
&lt;br&gt;
Let x be the hundreds digit;
then the tens digit is 2x (the tens digit is twice the hundreds digit);
then the units digit is 2x-2 (it is 2 less than the tens digit)&lt;br&gt;
The value of the 3-digit number ABC is 100A+10B+C.  So an expression for the 3-digit number in this problem is&lt;br&gt;
100(x)+10(2x)+1(2x-2)&lt;br&gt;
Simplify if required....&lt;br&gt;
Note that x and 2x are both single-digit positive integers; that means x can have only the values 1, 2, 3, or 4.&lt;br&gt;
Those values of x in the expression shown will produce all of the 3-digit numbers that satisfy the conditions of the problem.&lt;br&gt;
120
242
364
486&lt;br&gt;
Another completely different way to solve the problem is to make a list of the 3-digit numbers that satisfy the given conditions and find an algebraic expression that produces exactly that list.&lt;br&gt;
Making the list is relatively easy; choose a hundreds digit; then the tens digit is twice the hundreds digit; then the units digit is 2 less than the tens digit:&lt;br&gt;
1; 1*2 = 2; 2-2 - 0  --&gt;  120
2; 2*2 = 4; 4-2 = 2  --&gt;  242
3; 3*2 = 6; 6-2 = 4  --&gt;  364
4; 4*2 = 8; 8-2 = 6  --&gt;  486
5; 5*2 = 10 too big; the list is complete.&lt;br&gt;
The 3-digit numbers satisfying the given conditions are&lt;br&gt;
120, 242, 364, and 486.&lt;br&gt;
A bit of simple algebra, seeing the first number 120 and a common difference of 122 between successive numbers in the list, yields the linear expression&lt;br&gt;
122x-2&lt;br&gt;
which is the simplified form of the expression shown above.

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