Question 1207335
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Here is a very unorthodox method for solving a problem like this....  A bit difficult to learn; but if you can learn it, it is much faster than the formal algebraic solution method.  Of course, if a formal algebraic solution is needed, this won't help you.<br>
We can treat this as a "mixture" problem -- we are "mixing" pens that cost $2.50 each with pens that cost $8.50 each to get a "mixture" of pens that cost an average of $4.50 each.<br>
For an unorthodox method for solving that problem, look at the three numbers 2.50, 4.50, and 8.50 (on a number line, if it helps) and observe/calculate that 4.50 is 1/3 of the way from 2.50 to 8.50 (from 2.50 to 8.50 is a difference of 6; from 2.50 to 4.50 is a difference of 2; 2/6 = 1/3).<br>
That means 1/3 of the pens were the more expensive ones.  Then, since there was one $8.50 pen, the total number of pens was 3.<br>
ANSWER: 3 pens (1 at $8.50 and 2 at $2.50 each)<br>
CHECK:
$8.50 + 2($2.50) = $13.50
3($4.50) = $13.50<br>