<PRE><B>Question 1182018</B>
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In the response from the other tutor, they wrote down three equations in three variables directly from the information as given in the problem.  Then they showed starting the process of solving the problem by playing with those equations to determine that the number of roses should be 50. (And they go no further with their response....)&lt;br&gt;
That is a valid way to start on an algebraic solution to the problem.  But there are much better ways!&lt;br&gt;
If you read the problem and take a few seconds to analyze the given information, you will realize that &quot;she also wants to buy 100 items in total&quot; and &quot;she also wants the combined number of chocolates and balloons to be equal to that of roses&quot; together immediately tell you that the number of roses is 50 -- and also that the total number of chocolates and balloons is also 50.&lt;br&gt;
The lesson there is this:&lt;br&gt;
Read and understand the problem before you start writing equations!&lt;br&gt;
Now the setup is easy, using a single variable:&lt;br&gt;
50 = # of roses
c = # of chocolates
50-c = # of balloons&lt;br&gt;
That gives us a single equation to try to solve:&lt;br&gt;
50(35)+25(c)+25(50-c) = 3000&lt;br&gt;
But trying to solve that equation shows that the problem is faulty:&lt;br&gt;
1750+25c+1250-25c = 3000
3000 = 3000&lt;br&gt;
This equation tells us nothing that we did not already know.  And there is no information given that we haven&#39;t used, so we can&#39;t go any farther with the solution.&lt;br&gt;
The fact that the prices of a chocolate and a balloon are the same makes it impossible to find a single answer to the problem.&lt;br&gt;
In fact, from the given information, we can only tell that the number of roses must be 50 and the combined numbers of chocolates and balloons must be 50.&lt;br&gt;
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