Question 275471
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The first of two numbers is one more than twice the second. The sum of twice the first number 
and three times the second number is 51. Find the numbers.
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        In his post, @mananth missed first and second number and produced wrong answer 

        " x=6 for the first number and 2x = 2*6 = 12 for the second number ".


        I came to provide a correct and accurate solution.



<pre>
Let the second number be x

Twice the second = 2x

One more means 2x+1. This is the first number.

Twice the second number = 2x


The equation for the sum of twice the first number 
and three times the second number is

    2(2x+1) + 3x = 51.


Simplify and find x

    4x + 2 + 3x = 51

    7x = 51 - 2
    
    7x = 49

     x = 49/7 = 7 is the second number

    2*x+1 = 2*7+1 = 15 is the first number



<U>ANSWER</U>.  First number is 15; second number is 7.
</pre>

Solved correctly.