SOLUTION: The sum of two integers is 74. The larger is 26 more than twice the smaller. Find the two integers.

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Question 1152591: The sum of two integers is 74. The larger is 26 more than twice the smaller. Find the two integers.
Answer by ikleyn(52878) About Me  (Show Source):
You can put this solution on YOUR website!
.

Mental solution 

From 74, subtract 26.  The difference,  74-26 = 48,  is 3 times the smaller number.


Hence, the two numbers are  48%2F3 = 16  and  2*16+26 = 32+26 = 58.    ANSWER


CHECK.  16 + 58 = 74.    ! Precisely correct !

Solved.


Algebra solution 

Let x be the smaller number.  

Then the other number is  2x+26.


The equation is


    x + (2x + 26) = 74


Simplify and solve


    x + 2x = 74 - 26

    3x = 48

     x = 48%2F3 = 16,


giving you the same answer.

Solved.

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Notice that the  Algebra solution  follows step-in-step the  Mental solution.

They both are  EQUIVALENT.