<PRE><B>Question 1162557</B>
&lt;br&gt;
This problem can give you good practice for setting up a problem for solving using formal algebra, and for then solving the problem.  You should learn how to do that.&lt;br&gt;
(1) The sum of three numbers is 17.
{{{a+b+c = 17}}}&lt;br&gt;
(2) The sum of twice the first​ number, 3 times the second​ number, and 4 times the third number is 49.
{{{2a+3b+4c = 49}}}&lt;br&gt;
(3) The difference between 3 times the first number and the second number is 21.
{{{3a-b = 21}}}&lt;br&gt;
There are numerous ways of solving that system of three equations to find the values of a, b, and c.  Because of that, I will only show one possible way to start on that task.  You can finish the way I show; or you can use a completely different path if you want.&lt;br&gt;
With the form of the three equations, my preference would be to solve (3) for b and substitute the result in (1) and (2); that will give me two equations in a and c.&lt;br&gt;
{{{3a-b = 21}}}
{{{b = 3a-21}}}&lt;br&gt;
Substituting in (1):
{{{a+(3a-21)+c = 17}}}
(4) {{{4a+c = 38}}}&lt;br&gt;
Substituting in (2):
{{{2a+3(3a-21)+4c = 49}}}
(5) {{{11a+4c = 112}}}&lt;br&gt;
Solve (4) and (5)....&lt;br&gt;
This problem also gives you an excellent opportunity to get some good mental exercise by finding a solution using logical reasoning and some basic arithmetic.  Here is how it might go.&lt;br&gt;
To start, the nature of the question suggests that the three numbers are positive integers.  So let&#39;s assume that.&lt;br&gt;
The sum of the three numbers is 17; and the difference between 3 times the first number and the second number is 21.  With our assumption that the three numbers are positive integers, the smallest possible value for the first number is 8.&lt;br&gt;
If the first number is 8, the second number is 3 (to make the difference between 3 times the first number and the second number 21).  And, since the sum of the three number is 17, that means the third number is 6.&lt;br&gt;
The possible solution (8,3,6) satisfies (1) and (3); and checking it in (2) we see that requirement is also satisfied.&lt;br&gt;
So we have found the solution by logical reasoning, without formal algebra.&lt;br&gt;
ANSWER: The three numbers are 8, 3, and 6.&lt;br&gt;
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