<PRE><B>Question 1170013</B>
&lt;br&gt;
(1) Using formal algebra....&lt;br&gt;
x = # articles at $2 each
(14-x) = # articles at $2.25 each&lt;br&gt;
{{{x(2.00)+(14-x)(2.25) = 30.00}}}&lt;br&gt;
Solve using basic algebra.&lt;br&gt;
You should certainly know how to set up and solve the problem like that, or in another similar way, using formal algebra.&lt;br&gt;
If a formal algebraic solution is not required (for example, in a timed math competition where getting an answer as fast as possible is desired), there are many other ways to solve the problem.&lt;br&gt;
(2) Informally, using logical reasoning and some simple arithmetic....&lt;br&gt;
All 14 articles at $2.00 each would be $28.00, which is $2.00 short of the actual total.
Each of the articles selling for $2.25 costs $0.25 more than one selling for $2.00.
The number of articles selling at $2.25 each, in order to make up the additional $2.00, is $2.00 divided by $0.25, which is 8.&lt;br&gt;
ANSWER: 8 articles at $2.25 each and 14-8=6 articles at $2.00 each.&lt;br&gt;
CHECK: 8(2.25) + 6(2.00  = 18+12 = 30&lt;br&gt;
(3) And yet another solution using logical reasoning....&lt;br&gt;
The total cost is an even whole dollar amount; and the total cost of any number of $2.00 items will be an even whole dollar amount.
So the total cost of the items at $2.25 each must be an even whole dollar amount.
The only number of items (less than 14) at $2.25 each for which the total is an even whole number of dollars is 8: 8($2.25) = $18.&lt;br&gt;
So there must be 8 items at $2.25 each and 14-8=6 items at $2 each.&lt;br&gt;
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